The past decade has witnessed an explosive growth of data and the needs for high-speed data communications and processing. The needs continue to drive the development of new hardware for transmitting more data reliably and processing more data to obtain a higher level of intelligence. This thesis work explores algorithm-architecture co-design approach to derive efficient solutions for domain-specific communication and machine learning accelerators. It focuses on advanced and most compute-intensive accelerator designs for: 1) channel coding for data transmission, including polar codes and low-density parity-check (LDPC) codes, and 2) neural networks for machine learning, including differentiable neural computer (DNC) and neural ordinary diff...