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) graph filters, including the recently developed node-varying and edge-varying extensions. Further, we will discuss autoregressive moving average (ARMA) graph filters, which can approximate a desired frequency response much better than FIR graph filters of the same order, and which give exact solutions for some specific graph signal denoising and interpolation tasks. Numerical results will accompany the theoretical findings, showing that node- and edge-varying FIR filters as well as ARMA filters are appealing alternatives for the conventional FIR graph filters.