Ionic propulsion is an emerging technology in the aerospace field. An ionic thruster is based on a corona discharge mechanism that generates an ionic wind, which in turn produces the required thrust. The physical process underlying corona discharge is the ionization of air molecules induced by a strong electric field. Free electrons play a crucial role in the ionization process. These phenomena and their mathematical modeling are currently being investigated within the framework of the IPROP project led by Politecnico di Milano. In this talk, we introduce the concept of corona discharge and discuss its main phenomenological aspects. Starting from the physical understanding of the underlying mechanisms, mathematical models with different levels of approximation will be presented. The second part of the talk will focus on suitable spatial discretization techniques designed to address the numerical difficulties arising in strongly drift-dominated regimes. Finally, the application to ionic propulsion will be discussed, with particular emphasis on the coupling between the electric problem and fluid dynamics, which is essential for accurately predicting the generated thrust