  The aim of this article is to prove asymptotic shape theorems for the contact
process in stationary random environment. These theorems generalize known
results for the classical contact process. In particular, if H_t denotes the
set of already occupied sites at time t, we show that for almost every
environment, when the contact process survives, the set H_t/t almost surely
converges to a compact set that only depends on the law of the environment. To
this aim, we prove a new almost subadditive ergodic theorem.
