Academic (set in cities noted for their rivers and universities)
HistoryNot necessarily actual historical variants, but variants with historical themes.
Mathematics & Science (Physics/Chemistry/Astronomy)
Cinema(see also literature for e.g. LOTR-themed variants)
Not just variants with an SF/F flavour in the rules, but also those arising out of an SF/F setting. For example, there is nothing overtly fantastic about Gothic Isles Chess (apart from the names of some of the pieces), but it was developed as part of a Fantasy setting and so belongs here. Much the same applies to Star Trek 3-Dimensional Chess. On the other hand, mere names of pieces are not enough to qualify a variant as SF/F, since so many variants have Fantasy-style piece names that it would become meaningless to include all of them e.g. Omega Chess would not belong here. Finally, I have included Dunsanys Chess purely because its inventor, Lord Dunsany, was a famous Fantasy writer.
Wargames/RoleplayingGiven the origins of Chess as a wargame, all variants are in a sense wargames too. However, I am talking about variants that are influenced by modern wargames/RPGs, with their emphasis on realistic simulation (as opposed to the relatively abstract and symbolic nature of most members of the Chess family). Variants included in this category tend to borrow modern wargame/RPG concepts like attack/defence factors, missile fire, promotion to higher levels, hit points, the role of chance, fog of war, etc.