  In the first part of the paper, we discuss different versions of the AdS/CFT
dictionary out of equilibrium. We show that the Skenderis - van Rees
prescription and the "extrapolate" dictionary are equivalent at the level of
"in-in" two point functions of free scalar fields in arbitrary asymptotically
AdS spacetimes. In the second part of the paper, we calculate two point
correlation functions in dynamical spacetimes using the "extrapolate"
dictionary. These calculations are performed for conformally coupled scalar
fields in examples of spacetimes undergoing gravitational collapse, the
AdS$_2$-Vaidya spacetime and the AdS$_3$-Vaidya spacetime, which allow us to
address the problem of thermalization following a quench in the boundary field
theory. The computation of the correlators is formulated as an initial value
problem in the bulk spacetime. Finally, we compare our results for
AdS$_3$-Vaidya to results in the previous literature obtained using the
geodesic approximation and we find qualitative agreement.
