We analyze neocortical dynamics using field theoretic methods for non-equilibrium statistical processes. Assuming the dynamics is Markovian, we introduce a model that describes both neural fluctuations and responses to stimuli. We show that at low spiking rates, neocortical activity exhibits a dynamical phase transition which is in the universality class of directed percolation (DP). Because of the high density and large spatial extent of neural interactions, there is a "mean field" region in which the effects of fluctuations are negligible. However as the generation and decay of spiking activity becomes balanced, there is a crossover into the critical fluctuation driven DP region, consistent with measurements in neocortical slice preparations. From the perspective of theoretical neuroscience, the principal contribution of this work is the formulation of a theory of neural activity that goes beyond the mean-field approximation and incorporates the effects of fluctuations and correlations in the critical region. This theory shows that the scaling laws found in many measurements of neocortical activity, in anesthetized, normal and epileptic neocortex, are consistent with the existence of DP and related phase transitions at a critical point. It also shows how such properties lead to a model of the origins of both random and rhythmic brain activity.