Abstract: Any departure from scale invariance in the statistics of primordial fluctuations can be understood as the result of particle production during inflation. In this talks I will provide a general framework to study the excitation of states (particle production) along the evolution of the primordial curvature fluctuations with Bunch-Davies initial conditions. I will show that the dynamics of particle production can be studied in terms of first order differential equations governing the evolution of Bogoliubov coefficients describing self-interactions of the curvature perturbation (due to Hubble flow dynamics) and/or its interactions with other fields (due to multi-field dynamics). These equations allow us to obtain general templates parametrizing features in the primordial statistics, for instance the power spectrum/bispectrum of curvature perturbations or the spectrum of gravitational waves generated during inflation.