Hawkes processes are a class of point processes used to model self-excitation and cross-excitation between different types of events. They are characterized by the auto-regressive structure of their conditional intensity, and there exists several extensions to the original linear Hawkes model. In this talk, we start by defining Hawkes processes and give a brief overview of some of their basic properties. We then review some approaches to parametric and non-parametric estimation of Hawkes processes and discuss some applications to problems with large data sets in high frequency finance and social networks.