Abstract The transition from analog telecommunication equipment and terminals to digital systems and, more recently, the fast development of wireless communications were made possible by three factors: 1) key advances in integrated circuit technology, 2) large improvements in methodologies and tools for the design of highly complex digital circuits, and 3) progress in information theory, in particular, the belief propagation algorithm that allows error control codes operating close to the Shannon limit. In this chapter, an overview of architecture of turbo and LDPC codes is presented. The standard implementation (i.e., low complexity) of those codes is first presented. Then architecture for high-speed, low-power, and high flexibility are derived. Finally, the chapter concludes with the presentation of exotic decoding architectures and a survey of relevant architectures. Keywords