Some really really nice things in Resolution of singularities (tribute to Zariski), ed Hauser, Lipman et al. Progress in Mathematics.
An improved version of the alteration thm comes from Gabber’s work on purity, see maybe study group notes of Riou or maybe Illusie. Or ask Riou. It was something along the following lines: Take any quite general scheme, and a prime l. Then there exist an alteration of degree prime to l (this is not exactly right, so check proper ref).
http://mathoverflow.net/questions/27821/alterations-of-regular-varieties
The work of Gabber (see Illusie et al on arXiv) contains applications of alterations.
nLab page on Alterations