The primary objective of the present paper is to provide a brief survey of basic ideas and some key results of the theory of Hawkes processes that may serve as an interface for multidisciplinary research between mathematics and neurosciences, with hints to epidemiology. The class of Hawkes processes is considered as an appropriate model to describe the pattern of neuronal firing, see [56] [38]. As such, it is a prime candidate for detecting changes in brain activity, and consequently to predict epileptic seizures. Most of the advanced results will be presented via simple examples. In addition, we elaborate on links between the theory of Hawkes processes and linear stochastic systems, in particular system identification. A few new results in this context will be also presented with the outline of their proofs.