This review focuses on penalized learning methods for estimating models of temporal and spatio-temporal point processes. These methods find applications in a great variety of fields, such as in geostatistics, neuroscience, epidemiology, econometrics, social science, etc., wherein the availability of large and complex datasets is growing and advanced statistical methodologies are needed. However, typical solutions involve, for instance, the direct maximization of the log-likelihood, which suffers from well-known high computational costs and poor statistical properties for high-dimensional parameters. In this chapter, we review a series of works aiming at circumventing some of those limitations by penalized learning, possibly replacing the log-likelihood by the quadratic contrast.