  We introduce a formalism, valid both for dark matter and collapsed objects,
that allows us to describe redshift space distortions in the context of the
Effective Field Theory of Large Scale Structures (EFTofLSS). Expressing density
perturbations in redshift space corresponds to performing a change of
coordinates and the resulting expressions contain products of density
perturbations and velocity fields evaluated at the same location. These terms
are sensitive to non-perturbative short-distance physics and in order to
correctly treat them they need to be renormalized by adding suitable
counterterms. Therefore more counterterms are required in redshift space
expressions compared to their real space analogs. In particular in the
expression for the one-loop matter power spectrum there are two new
counterterms. Just as in real space, long wavelength displacements affect
correlation functions in redshift space and need to be resummed. We generalize
the real space formulas for IR resummation to this case: the final expressions
are conceptually similar but are more challenging to compute numerically due to
their reduced symmetry.
