Olympus - not like anybody else..

Olympus as a company was founded in October 1919, the same year as Asahi Optical (Pentax). They started as a producers of microscopes and thermometers under the name Orinpasu Kabushiki-gaisha, but went into camera production in 1936, mainly producing medium format cameras. In 1949 the company was renamed to Olympus Optical Co, Ltd.
When everyone else started making Pentprism slr cameras, Olympus came up with the Pen, a small 35 mm compact. The format was 18x24, 35mm cut in half and giving 72 shots on one 36 frames roll. This was in 1959, the year of the Nikon F. A brave move indeed. In 1963 the Pen-F was launched, an porro prism slr camera. It sold a lot, as the quality was very good and the cameras came with very high quality Zuiko lenses. Besides, they were small and light compared to most other brands.
Still, even if the lenses were good, the half-format couldn't match the 35mm for the pros when they demanded the best. So in 1972 Olympus finally, as the last of the existing brands, introduced their PP SLR answer. The idea of making small and light cameras was followed up when they presented the M-1. Measuring only 136x83x50 mm and weighing only 510 grams, this was the smallest and lightest PP SLR ever. Other brands had to come up with an answer, and Pentax made the ME, even smaller and lighter. But that was some four years later, and Olympus had made themselves a name, taking a big bite of the market. 
By naming the camera M-1 Olympus had challenged Leica, who owned the right to M as a model name. Leica warned them of trouble to come, and Olympus soon renamed their M to OM.
 

Olympus had great success with the OM-series. After OM-1 followed OM-2 in 1975, introducing a new metering system, Auto Dynamic Metering (ADM), and an improved flash-metering. 
1983 saw the OM-3, with spot metering added to the earlier average metering system. This camera was soon followed by the OM-4 with multi- spot metering. In 1986 came the OM-4 Ti with a titan house. This model was produced till as late as 2002.

However, Olympus wasn't prepared for the auto-focus revolution, and never responded to it with top-of-the-line film cameras. Once again, as with the introduction of the Japanese PentaPrism SLR in the 50s, Olympus was falling behind. Their answer was several bridge-cameras, but they could not keep up with the quality cameras of the competition.

At last, in 2003, Olympus was ready for a comeback. They introduced their E-1, a digital, professional system. They didn't follow Canon and Nikon with full frame format, but, typically for Olympus, invented the Four-Thirds-system. (Later to be joined by Panasonic.) That was even smaller than the APS-C format that other brands used. Good for smaller size and lower weight, worse for quality enlargements. History repeats itself: the Pen of the early 60's.

After E-1 followed E-3 in 2007 and E-5 in 2010, improved each time. These were high-end cameras. Olympus also produced many less advanced models, ending with E-620 in 2009.

In 2013 Olympus declared they were leaving the PentaPrism DSLR market and concentrating on mirrorless cameras. That is why I set their PP SLR history to be 1972-2013. 

On June 24th 2020, Olympus officially stated they were selling their camera division to Japan Industrial Partners. A final agreement has been signed on September 30th, revealing that the name of the JIP's camera division will be OM Digital Solutions Corporation, and that the Olympus factory in Vietnam will continue to produce for the new owners. New products already announced will be produced under the new brand name.
That is what we know by now, October 1st 2020. 

Anyway, like Minolta and Konica in 2006, Olympus as a camera brand is now history.