  We discuss higher derivative corrections to black hole entropy in theories
that allow a near horizon AdS_3 x X geometry. In arbitrary theories with
diffeomorphism invariance we show how to obtain the spacetime central charge in
a simple way. Black hole entropy then follows from the Euclidean partition
function, and we show that this gives agreement with Wald's formula. In string
theory there are certain diffeomorphism anomalies that we exploit. We thereby
reproduce some recent computations of corrected entropy formulas, and extend
them to the nonextremal, nonsupersymetric context. Examples include black holes
in M-theory on K3 x T^2, whose entropy reproduces that of the perturbative
heterotic string with both right and left movers excited and angular momentum
included. Our anomaly based approach also sheds light on why exact results have
been obtained in four dimensions while ignoring R^4 type corrections.

High Energy Physics - Theory;General Relativity and Quantum Cosmology