We introduce non-stationary Hawkes processes which are defined similarly to standard Hawkes processes but with a time- (or space-)evolving base intensity and fertility function. The resulting process is inhomogeneous. However the usual conditions for the existence of a stationary Hawkes process are easily adapted to obtain a stable non-stationary model. A wildly non-stationary model cannot be consistently inferred, even from an infinite sample of data. Having in mind the statistical analysis of non-stationary Hawkes processes, we propose an approach inspired from locally stationary time series. We are thus interested in an asymptotic framework where the dimension of the observation windows tend to infinity while the time- (or space-)varying parameters are sampled from a function whose corresponding support remains unchanged. We show that under simple assumptions, the statistical properties of the locally stationary Hawkes process can be approximated by those of a stationary Hawkes process. In particular, this framework allows us to propose a time-frequency analysis of Hawkes processes with time varying parameters.