Advances in astronomy are intimately linked to advances in digital signal processing (DSP). This special issue is focused upon advances in DSP within radio astronomy. The trend within that community is to use off-the-shelf digital hardware where possible and leverage advances in high performance computing. In particular, graphics processing units (GPUs) and field programmable gate arrays (FPGAs) are being used in place of application-specific circuits (ASICs); high-speed Ethernet and Infiniband are being used for interconnect in place of custom backplanes. Further, to lower hurdles in digital engineering, communities have designed and released general-purpose FPGA-based DSP systems, such as the CASPER ROACH board, ASTRON Uniboard and CSIRO Redback board. In this introductory article, we give a brief historical overview, a summary of recent trends, and provide an outlook on future directions.