It is now well established that the complex environments around many massive stars can directly affect the observed properties of their supernova (SN) explosions. I will provide a review on the detailed physics of interacting SNe powered by the collision between SN ejecta and circumstellar material (CSI) and the resulting electromagnetic signal in the form of broad-band light curves and spectra. I will then present our group's work on calculating models of light curves, spectra and individual emission line profiles associated with CSI for a variety of initial conditions for both the progenitor star (mass, explosion energy) and the circumstellar material (mass, density profile and composition). Special attention will be given on modeling the emission line profile of the Hα line associated with radiative recombination including the effects of top illumination by the forward shock that is formed during the interaction. Finally, I will discuss the implications of our results on the understanding of luminous fast blue transients and super-luminous supernovae of both the H-poor (SLSN-I) and H-rich (SLSN-II) type and outline our plans to model spectra of interaction-powered supernovae in two and three dimensions for a range of circumstellar envelope geometries.