Jardine-Goerss chapter IV. Source of spectral sequence constructions, e.g. the Serre spectral sequence. There are many model structures, for example the Bousfield-Kan (pointwise WEs), the Reedy (pointwise WEs), the Moerdijk (diagonal WEs), and the E2 structures. Other spectral sequences include the Bousfield-Friedlander, which is in fact a reindexed version of the Bousfield-Kan ss for a tower of fibrations.
nLab page on Bisimplicial sets