Cohomological descent

In algebraic geometry, a cohomological descent is, roughly, a "derived" version of a fully faithful descent in the classical descent theory. This point is made precise by the below: the following are equivalent: in an appropriate setting, given a map "a" from a simplicial space "X" to a space "S", 
The map "a" is then said to be a morphism of cohomological descent.
The treatment in SGA uses a lot of topos theory. Conrad's notes gives a more down-to-earth exposition.