In recent years Dynamic Stochastic General Equilibrium models have come to play an increasing role in central banks, as an aid in the formulation of monetary policy (and increasingly after the global crisis, for maintaining financial stability). DSGE models, it is claimed, are less a-theoretic than other widely used models such as VAR, or dynamic factor models. As the models are "structural," they are supposed to be immune to the Lucas Critique, and thus can be "taken to the data" in a meaningful way. However, a major feature of these models is that their theoretical underpinnings lie in what has now come to be called as the New Consensus Macroeconomics. Using the prototype real business cycle model as an illustration, this paper brings out the econometric structure underpinning such models. A detailed analytical critique is also presented together with some promising leads for future research.