I am learning to compute cohomology of finite groups and came across this survey article http://www.ams.org/notices/199707/adem.pdf "Recent Developments in the cohomology of finite groups" by Alejandro Adem and various other articles by him on calculations of cohomology of finite groups. There is also a book by Adem and Milgram in which they compute cohomology of many finite groups. I would like to know

To what extent the cohomology of finite groups is known. Is it for example known for every finite simple group (in the classification). Any reference on the list of finite groups with known (unknown) cohomology will be nice.

I do apologize if the question is too simple to ask for this forum.