For a few references in English, there are the papers of Heller, the main one being:
A. Heller, Homotopy theories, Mem. Amer. Math. Soc. 71 (383) (1988)
There is also a paper I wrote with A. Neeman, in which there is a little introduction to derivators in the second half of:
Additivity for derivator K-theory, Adv. Math. 217 (2008), no. 4, 1381-1475
One can see derivators in action in the work of G. Tabuada (he explains Bousfield localization and stabilization in this setting, and compares with the model category point of view):
Higher K-theory via universal invariants, Duke Math. J. 145 (2008), no. 1, 121–206
(availabe as arXiv:0706.2420).
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