Forward-Error-Correction (FEC) constitutes a dominant power consuming and throughput limiting component in the end-to-end digital baseband chain for wireless systems. With the progress in THz and Tbit/s link-level technologies towards practical solutions and deployments arguably in beyond-5G and 6G era, the performance and implementation bottleneck due to FEC in these systems becomes increasingly clear. In this paper, we explore FEC performance requirements for various beyond-5G wireless use-cases from a practical implementation perspective. We then provide some recent designs in Low Density Parity Check (LDPC) and Polar Codes, and their decoder architectures that demonstrate significant potential towards achieving throughputs approaching 1 Tbit/s.