Biological theories - in such theories biology is key factor. For example: scientific racism (Arthur de Gobineau), Social Darwinism (Herbert Spencer), or theories where you treat civilisations like a living organism that always have to go through 3 phases: youth/development, adulthood/prosperity, senility/decline (for example Oswald Spengler theory).
Economical theories - economy as key factor. For example: Liberalism, Marxism, etc. Right now those theories are very popular, a lot of people assume that there is actually one big human civilisation and differences are just in economic level of each country/region/group.
Ideological theories - ideology/religion as key factor. Examples: Christianity, Islam, Freemasonry, Cultural Marxism, etc.
There were also attempts to merge all of those aspects: Toynbee, Koneczny (someone mention his work in one of the comments), Huntington (personally I think he ineptly copied Koneczny work).
Because of Pax Americana after WWII most people start belive that liberal democracy and capitalism was finall destination of all civilisations (Fukuyama famous book: "End of history"). But right now with rise of China and their model of state/economy/politics people start looking for much broader theories.