There really isn't a style of swordsmanship that uses it all the time, but there are situational uses for the reverse grip that are historically documented.

Fiore dei Liberi holds the sword in a reverse grip with the purpose of wanting to throw the sword like a javelin which [Skallagrim has demonstrated before on his channel.][1]

[![enter image description here][2]][2]

Historical Japanese and Chinese swordsmanship occasionally seems to show it used for certain situations:

[![enter image description here][3]][3]

[![enter image description here][4]][4]

And in iaido/iaijutsu it is occasionally done, but primarily as a method of returning the sword comfortably and also during very specific situations when the sword can **only** be retrieved in a reverse grip:

[![enter image description here][5]][5]

The reverse grip is especially important if you want to comfortably draw and sheathe an especially long sword since it will allow a tighter angle to be made when drawing/sheathing without putting too much strain on your wrist.

[![enter image description here][6]][6]

It also is occasionally done on particularly short "swords" [like butterfly swords from Wing Chun][7] and seems to be done as a way to use your forearms as a blocking tool kind of like how a tonfa would work.

[![enter image description here][8]][8]

Keep in mind with all the examples given though; they are situational moves designed to supplement holding the sword the normal way and not something that is done all the time like seen in fiction-land. :P

  [1]: https://www.youtube.com/watch?v=QYVIsMQPKzY
  [2]: https://i.sstatic.net/sxrMc.jpg
  [3]: https://i.sstatic.net/UahAx.jpg
  [4]: https://i.sstatic.net/uUQHz.jpg
  [5]: https://i.sstatic.net/CYWzP.jpg
  [6]: https://i.sstatic.net/DFc4k.jpg
  [7]: https://www.youtube.com/watch?v=rAi2R7naa7A
  [8]: https://i.sstatic.net/B5iXz.jpg