  We generalize Penrose's notion of conformal infinity of spacetime, to
situations with anisotropic scaling. This is relevant not only for
Lifshitz-type anisotropic gravity models, but also in standard general
relativity and string theory, for spacetimes exhibiting a natural asymptotic
anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as
AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the
near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears
crucial for resolving puzzles of holographic renormalization in such
spacetimes.
