For computation-intensive digital signal processing algorithms, complexity is exceeding the processing capabilities of general-purpose digital signal processors (DSPs). In some of these applications, DSP hardware accelerators have been widely used to off-load a variety of algorithms from the main DSP host, including the fast Fourier transform, digital filters, multiple-input multiple-output detectors, and error correction codes (Viterbi, turbo, low-density parity-check) decoders. Given power and cost considerations, simply implementing these computationally complex parallel algorithms with high-speed general-purpose DSP processor is not very efficient. However, not all DSP algorithms are appropriate for off-loading to a hardware accelerator. First, these algorithms should have data-parallel computations and repeated operations that are amenable to hardware implementation. Second, these algorithms should have a deterministic dataflow graph that maps to parallel datapaths. In this chapter, we focus on some of the basic and advanced digital signal processing algorithms for communications and cover major examples of DSP accelerators.