Fifth-generation (5G) new radio (NR) holds promise in fulfilling new communication requirements that enable ubiquitous, low-latency, high-speed, and high-reliability connections among mobile devices. Compared to fourth-generation (4G) long-Term evolution (LTE), new error-correcting codes have been introduced in 5G NR for both data and control channels. In this article, the specific low-density parity-check (LDPC) codes and polar codes adopted by the 5G NR standard are described. The purpose of each key component in these codes and the associated operations are explained. Performance and implementation advantages of these new codes are compared with those of 4G LTE.