Hi Asher, Well that is perhaps a separate discussion, because there are more uses than I am maybe aware of, and I see a few UV photographers here on your site...
Often flowers are shot in UV to see other patterns that are not seen in the visual or IR spectrum.
The classic flower would be the Rudbeckia, which has a different pattern in UV, however there are a few Rudbeckia variations that show the pattern in visual these days.
UV photography should not be confused with fluorescence photography, which some people might think of as 'black light' photography, or more technically UVIVF (UV induced visual fluorescence).
In this topic you have three people, each of which sell their own versions of UV filters.
And then there are UV+Blue, and UV+Blue+Green, and UV+...
Probably the old 'industry standard' UV-Only filter, the Baader U, which is the UV-A range, and that is the range that almost all older UV capable lenses will transmit, 320nm and above.
Unless you have a very special lens, then any UV filter that transmits below the 320nm to 400nm range is truncated by the lens, and doesn't reach its potential range.
There are more expensive special lenses that transmit all the way down into UV-B and UV-C, but since our camera sensors don't reach that far it is pretty much pointless, but those lenses at least transmit down to 320nm on a flat curve, but 7 grand gets pricey, the Kuri 35mm I use works well for me, and there are other such lenses.
Most newer lenses however will not transmit UV well, and they may cut off UV at about 360nm or even 370/380/390nm... and with very weak amplitude.
The lens is the big bottleneck with UV photography, and a very important important item in the mix.
The camera of course needs to be converted to full spectrum, removing the BG internal glass replacing it with clear UV transmitting glass, and various places can do that, usually costing $300 to $450, depending on model, company, etc..
The two main places in the US are MaxMax and LifePixel, and some on eBay also.
Full spectrum conversions, which can be used for UV and IR, and returned to visual with BG filters.
Often used for astronomy also.
UV can be used for people's faces, landscapes, medical skin analysis, forensics, like I said before - flowers, plants, animals, insects...
UV is just the other end of the spectrum from IR, not quite as easy, because the sensor is not as sensitive to UV as it is to IR even when converted, so usually we need to use longer exposures with a tripod if we want UV pics with low ISO and less noise...
I come from the artistic perspective, even though I get kind of technical with all this, my tendency is to admire the art in everything photographic, but of course that can involve a lot of technical things.
Here is a UV photo of a red barn with white trim using a UV-only filter, probably a Baader U at that date. My favorite filter is the La La U, it looks the same as the Baader U when using a shared white balance, and has the same exposure time, at least with my Kuri 35mm, and much less expensive.