Digital signal processing has become essential to the design and implementation of high-performance audio, video, and multi-media signal processing. One of the essential drivers for cost effective implementation of DSP algorithms is the multi-rate filter. Many of us (mistakenly) believe that digital filters are simply sampled data counterparts of linear time-invariant analog prototype filters. The digital world is richer than this and offers us easy access to filters with time-varying coefficients. Such filters offer very efficient structures to perform digital filtering, spectral translation, interpolation, and decimation with both non-recursive and with recursive structures. This paper presents the essentials of multi-rate filtering along with applications and demonstrations.