Currently, surface acoustic wave (SAW) filters are widely used in RF stages as well as IF stages of modern telecommunication systems. With successful research and development of SAW devices since the early 1960s, the growth of mobile phone markets has accelerated, with surprising advances in SAW device technologies since the early 1990s. This article discusses how the filtering function of SAW devices is realized using various SAW propagation phenomena, and reviews the performance of current commercial SAW filters. First, SAW transversal filters are discussed. Starting from a brief discussion of their fundamentals, we describe achievable performance, impact of the substrate selection and the most recent advances of this type of filter. Next, filters based on SAW resonators are discussed. After giving basic ideas of SAW resonators, it is shown how SAW resonator filters are composed and designed using SAW resonators.