In Elemental, rather than discover new technologies, you re-discover ancient technologies that were long lost after the events of the Cataclysm. You re-discover these techs by producing Tech Knowledge points per turn and the best way to obtain these is to control Ancient Libraries. These libraries are the best source of knowledge, keep in mind that there are minimal amount of buildings that you can construct that actually create raw Tech points, instead most buildings increase the Tech Knowledge produced by a city by a certain percent.

Knowing this it becomes really important to control these libraries sooner than later if not risk falling behind Technology wise.

You can find a list of both the Empire and Kingdoms tech trees over in the Technologies page.
(WIP more to come)