Some useful information is in 

Chacholski, Scherer, Homotopy theory of diagrams, math/0110316 

This and further references with useful material are listed in the reference section at <a href="http://ncatlab.org/nlab/show/homotopy+limit">nLab: homotopy limit</a>. 

(By immediate dualization this applies to homotopy colimits, of course).