INTRODUCTION
Although celestial apparitions have been reported for centuries, it is really not until 1947 that the 'UFO phenomenon' really started.
In that year a private pilot by the name of Kevin Arnold was flying near Mount Rainier in Washington State and reported seeing disc-like objects. This was reported by the press as flying saucers. That term was previously used in a comic magazine and became associated with aliens visitors to Earth.

Also in the same year was the report of alien craft that crashed in Roswell, New Mexico. Early reports sensationalised the event. Later military reports stated that the debris was from a weather balloon, and this is confirmed by an image taken at the time which shows aluminium foil covered panels as used in radar reflectors carried below weather balloons.
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TIMELINE
Reports of UFO sightings abound on the internet. This timeline is of significant events in the UFO phenomenon.
1947

IDENTIFYING THE UNIDENTIFIED
There can be thousands of reports notified to different authorities each year. Probably 50% of these can be identified by qualified observers almost immediately. Another 40% can probably be identified if an investigator is available and spends sufficient time on an investigation.
A large number of UFOs turn out to be aircraft (planes, helicopters, drones, etc), birds, bright stars or planets, kites, parachutes, meteors, fireballs, ball lightning, balloons, satellite reentries, bright satellites, satellite glints, rockets, hoaxes, etc.
Often there is simply not enough information to make an identification.
Hoaxes make up a large number of UFO reports, and the number is increasing. Why do people make up reports? There are many reasons. One is to test the gullibility of the analyst. I remember that someone once submitted to me a piece of metal and said it had fall off a UFO, meaning an alien craft. Even a cursory inspection showed it was a piece of aluminium with straight sides that had been drilled through with several holes and then had an oxyacetylene torch played over it which had partially melted some of the metal. It was the worst attempt I had seen to create an 'unknown' artifact.
A more interesting case was when I received an image from a Venezuelan young man claiming he had found an artifact that he thought might be from a UFO. It was a large shell (ammunition) shaped object about 150mm long and 20 mm in diameter. It was not metallic however, but made of compacted sand grains stuck together over many years. It obviously had been a copper shell originally that had accumulated the sand though a hole and then all copper had eventually dissolved away leaving the sand 'shell'. I was very circumspect in trying to explain all of this and told the person I knew he might find this hard to believe, but in fact he took it very well.
On another occasion I received a call from a farmer on the south coast of Western Australia who had some material fall from the sky on his property. It turned out to be classic radar reflector from a weather balloon - aluminium covered polystyrene. He accepted my analysis but I could see he was disappointed it wasn't an alien artifact.
LIGHTS IN THE SKY
I initially found it hard to believe that anyone could identify a stationary bright light in the sky as a UFO. But it happens very frequently. One evening as I was having dinner the phone range and the voice on the other end told me he was in Kings Park (Perth, Western Australia) and her had been observed this very bright UFO in the western sky for over an hour. I took a quick look outside and then came back and told him a few that there was a star near to the object and that the object was moving very slowly toward the horizon. The observer was startled and asked me if I could see it too? (I was over 1200 km north of his location - a fact he knew). In astonishment, he asked "Can you see it too?". After I answered in the affirmative he was then ready to accept when I told him that the object was the planet Venus.
Venus varies greatly in brightness throughout the year. Sometimes it appears only in the morning hours before sunrise and sometimes it appears in the evening hours just after sunset. So there is a time when it is not seen in the evening sky for many days. And when it does appear after sunset in a big city the high sky horizon there means it is often not seen until it is high in the sky. This is just the time when it is closest to the Earth and thus at is brightest. This puts it at magnitude -4, the brightest object in the night sky save for the Moon. It is at this that most Venus "UFO reports" are made.
Bright moving lights are another thing. When I was an undergraduate I was driving with my girlfriend along an unpopulated outer suburban road in Melbourne, Victoria. All of a sudden we noted that there were dozens of lights moving around in the sky. On winding down the window we could not hear any noise. I jokingly remarked that finally the aliens had come. When I looked over to my companion I saw that she had her head bowed and was praying. Fortunately as we got closer to the lights I could see that there was mix of white, green and red. And I then realised that we were close to Melbourne's secondary airport. The white lights were the aircraft's landing lights and initially had overwhelmed the fainter green and red navigation lights. What we were seeing was many aircraft involved in practicing circuits and night landing procedures. The lady involved now has a PhD.
There is a wide range of atmospheric phenomena with which most people have no experience and which are often reported as a UFO. Lenticular clouds (which have the shape of lenses, or two saucers joined together) are often reported as UFOs. One friend once asked me why some clouds looked so like flying saucers and I jokingly replied that it was probably because they had alien spacecraft inside them, as a disguise.

Another common phenomenon is to take low light pictures through a glass window. This often reveals a group of lights next to the outside object of interest. The lights of course are behind and in the same room as the photographer. I have taken many such images myself to illustrate the effect. Such UFO images as shown below are usually readily identified by anyone familiar with the phenomena.

MEASUREMENTS
It is not uncommon for UFO reports, even from experienced people to make statements like "the object was 200 metres long and 500 metres away. It appeared to be travelling at over 500 km/hour." Or "the object was 2 km above me and about 50m in size".
What we need to understand is that in the case of unknown objects, we have no reference with which to indicate distances and speeds. We need to understand that even with two good working eyes, our stereoscopic vision extends to an absolute limit of about 30m. Beyond that there is no stereo-disparity between our two eyeballs. This means that most of the time our estimates of size and distance (as for when driving) are done based on experience. Experience and knowledge of how big known objects are against a known background.
If we were put in a dark room with a sphere of unknown size invisibly suspended before us (and slightly glowing so we could see it), most of us would have no idea of how far away it was and how big it was, even if it was within our 30m stereoscopic visual acuity range.
This basically means that if we encounter an unknown object in the sky we have no idea how big it is and therefore how far away it is. If it happens to move in front of a building say, building whose distance from us is known, we can then say it has to be closer to us than the distance to the building. Many people find this hard to accept, as they are only used to estimating distances in familiar situations where the distances are known from experience. No experience, no knowledge.
I give an example of this from experience. I was piloting a friend's aircraft on a night flight from Tucson, Arizona to Alamogordo, New Mexico. My friend was sitting next to me. In the middle of the flight I saw a very bright light just above us and travelling toward us. We were flying at an altitude of 10,000 ft, the maximum allowed for night flying without supplemental oxygen. My friend suggested we contact El Paso control for information about the aircraft flying toward us. It turned out to be a Boeing 737 flying at 30,000 feet - and it had its landing lights on. Which only went to show that our appreciation of the (known) situation was way out. We were not in any danger of collision, even though the object (for a time) seemed to be heading toward us. That is why we were flying 'on instruments' after having filed an IFR (Instrument Flight Rules) flight plan. What you may see out the cockpit in that case is irrelevant.
HOAXES
It is now very easy to fake images showing apparent UFOs of any shape.
However, even worse than this is the fakery that has gone in the past, and that still occurs, claiming to have seen aliens and even to have gone for a ride in a flying saucer and been abducted by aliens.
Some of these experiences may well be experiences that the participants really believe they have undergone, but many of them have been deliberately fabricated. A example is George Adamski who published three books about his travels to Mars, Venus, Jupiter and Saturn with his alien friends. The books were published worldwide and combined with a lecture circuit made George a deal of money.
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In the Australian outback there are often no fences around homesteads (which can spread over thousands of acres) and sheep and cattle are free to road. Signs are often erected on roads passing through these areas to warn motorists to be on the lookout for the animals. Pranksters have occasionally doctored these signs to give motorists a laugh. The sign below, near Exmouth on North West Cape, Western Australia was quickly taken down by the local shire following a complaint by the homestead owner who may have thought it might encourage further activities detrimental to his livestock. UFOlogists have long believed that the large high powered naval transmitter at the top of the cape attracts alien visitors.

THE UNEXPLAINED
Of the several lengthy UFO investigations that have been undertaken, there is a always a small fraction that have been unable to be explained. This fraction usually lies somewhere around five percent. The reaction of people to this unexplained remainder usually takes two divergent paths.
The 'scientific' explanation says that there is no reason and no evidence to believe that any of these reports indicate the presence of alien spacecraft or aliens visiting the Earth. No physical evidence has ever been presented of material debris that is different from materials we know exist on the Earth. As Carl Sagan famously said: "Extraordinary claims require extraordinary evidence".
In an analogy with something of which we unfortunately are well familiar, we might consider murders in a large city. How many of these are not solved? From a recent (2023) report on the web we find "The US homicide clearance rate, a metric used by the FBI to assess how many murders are solved, was nearly 58% in 2023." This means an incredible 42% of all murders in the US in 2023 went unsolved! And of all crime, murders are probably the one crime which receives the greatest attention and effort in an attempt to solve. Certainly more time and effort than has ever been given trying to explain UFO reports. Does anyone believe that aliens are responsible for this crime? Or even a small proportion of this crime?
On the other hand a significant percentage of people believe aliens are visiting the Earth and even appearing to people as shown by the books below. And probably some of these people do believe that aliens are responsible for some murders.
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With around half of all people in the US subscribing to this belief, despite the absence of any physical evidence we are led to conclude that there is a strong desire in many people to believe in alien visitors to Earth. Why is this so?
Many psychologists believe that a strong desire to believe in aliens is related to a strong desire to believe that life must have a purpose. Religion often satisfies that desire and so fewer people with strong religious beliefs have less desire to believe in aliens, so goes the hypothesis.
Many people like the idea of powerful beings able to influence our life. Maybe we can learn something from them? Maybe they will help us?
There is also another angle to this related to 'people power'. Scientists and 'better educated' people generally do not believe there are aliens walking around on Earth. But for many less educated folk the idea of an alien presence is empowering. This is one area in which they can claim that they know more than the 'arrogant' intelligentsia. They have seen the aliens and they know the answer to an important question that others don't.

There is another aspect that we haven't yet explored. That explanation says that the UFO phenomena does involve a small percent of real alien reports, and these leave no physical evidence because the aliens are not physical, they are spiritual, although they often times can and do manifest themselves to humans. This belief has been around for a long time and has only recently been tied to UFOs.
THE RELIGIOUS EXPLANATION
Without question the Holy Bible states that there is a spiritual world. God created a vast number of angels and many of these carry out God's will and protect humans that are obedient to God's law, given to mankind at Mount Sinai when God came down to Earth.
God also created super angelic beings, archangels, three of whom are mentioned in the Bible: Lucifer, Michael and Gabriel. These beings were created with free will, and one of them, Lucifer, rebelled. In his rebellion he managed to get one third of all the angels to follow him in his quest to knock God off his throne and become ruler of the universe himself. War in heaven raged and Lucifer's army destroyed a large amount of God's physical creation - the universe became without form and void.
Eventually God and the righteous angels prevailed and Satan (Lucifer renamed as the Adversary) was cast down to the Earth. He and his demonic angels are restrained in what they can do, but they can certainly appear to humans and even 'possess' some. Jesus Christ during his physical appearance on Earth qualified to replace Satan as the God of this world, and spent a lot of time in casting out demons from people. He also gave instructions on how to avoid Satan's influence.
So those who claim there are spiritual beings living on the Earth today have the backing of the scriptures.
Of course not all churches believe this.

NASA Independent Study Team on UAPs (2023)
REFERENCES
Australian Space Academy