If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories, then observations need not be simply applied to reconstructing the inflaton potential, V(phi), or a specific kinetic term, a
s in DBI inflation, but rather to reconstruct the inflationary action in its entirety. We discuss the constraints that can be placed on a general single field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian, L(X,phi), with X={1/2}partial_muphipartial^muphi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge partial L/partial X = c_s^{-1}.
