Let $F\rightarrow X\rightarrow B$ be a fibration. If we know very well the spaces $F$ and $B$ and wish to compute the homology of $X$. One possible tool is the Serre Spectral Sequence. However, it works under the condition that $\pi\_1(B)$ acts trivially on $H\_\*(F;G)$. If this condition ($\pi\_1(B)$ acts trivially on $H\_\*(F;G)$) does not hold, what other tools can one use to compute the homology of the homology of $X$?


In fact I am interested in the special case that all spaces in the fibration are $K(\pi,1)$ spaces. If any approach works for this particular case it would be wonderful.


Thank you! 



Computing the homology groups of spaces in a fibration
Repeating Mark Grant's comment, the spectral sequence when all spaces are $K(\pi,1)$s goes under the name Lyndon-Hochschild-Serre spectral sequence. 


Good references for this spectral sequence are:


D. Benson: Representations and Cohomology II: cohomology of groups and modules


L. Evens: The cohomology of groups


Loads of papers have been written about this spectral sequence: Calculating $E^2$, when it degenerates at $E^2$, differentials, extension problems, you name it.... But a lot of the details depend on which class of groups $\pi$ you are interested in, so it's hard to give specific pointers without more information.


