TITLE: Künneth theorem for fibred products
QUESTION [7 upvotes]: Given the fibred product of two manifolds over a base space $X\times_Y Z$ , is there an analogue of Künneth theorem that allows one to compute the cohomology of the fibred product?

REPLY [5 votes]: The Eilenberg-Moore spectral sequence can be understood as a parametrized K\"unneth theorem. There is a monograph (also a paper) by L. Smith giving this approach (Lectures on the EMSS, Springer LNM 134, 1970).  Section 22.7 of http://www.math.uchicago.edu/~may/EXTHEORY/MaySig.pdf gives a new conceptual construction and a long list of relevant references.