  Two dimensional Warped Conformal Field Theories (WCFTs) may represent the
simplest examples of field theories without Lorentz invariance that can be
described holographically. As such they constitute a natural window into
holography in non AdS space-times, including the near horizon geometry of
generic extremal black holes. It is shown in this paper that WCFTs posses a
type of boost symmetry. Using this insight, we discuss how to couple these
theories to background geometry. This geometry is not Riemannian. We call it
Warped Geometry and it turns out to be a variant of a Newton-Cartan structure
with additional scaling symmetries. With this formalism the equivalent of Weyl
invariance in these theories is presented and we write two explicit examples of
WCFTs. These are free fermionic theories. Lastly we present a systematic
description of the holographic duals of WCFTs. It is argued that the minimal
setup is not Einstein gravity but an SL(2,R) x U(1) Chern-Simons Theory, which
we call Lower Spin Gravity. This point of view makes manifest the definition of
boundary for these non AdS geometries. This case represents the first step
towards understanding a fully invariant formalism for W_N field theories and
their holographic duals.
