One of the cornerstones of the field of graph signal processing are graph filters, direct analogues of time-domain filters, but intended for signals defined on graphs. In this talk, we will give an overview of the graph filtering problem. More specifically, we look at the family of finite impulse response (FIR) and infinite impulse response (IIR) graph filters and show how they can be used for different applications. Next, the concept of graph stationarity is introduced, which facilitates the analysis and processing of random graph signals. This is a challenging task due to the irregularity of the underlying graph domain. Firstly, coexisting stationarity definitions are presented along with explanations of their genesis, advantages, and disadvantages. Secondly, we introduce the concept of power spectral density for graph processes and propose a number of methods to estimate it. These methods include nonparametric approaches such as correlograms, as well as parametric approaches. Finally, we illustrate our covariance and power spectral density estimation schemes in synthetic and real-world graphs.