Versatile Video Coding (VVC)/H.266, completed in 2020, provides half the bitrate of the previous video coding standard (i.e., High-Efficiency Video Coding (HEVC)/H.265) while maintaining the same visual quality. The primary goal of VVC/H.266 is to achieve a compression capability that is noticeably better than that of HEVC/H.265, as well as the functionality to support a variety of applications with a single profile. Although VVC/H.266 has improved its coding performance by incorporating new advanced technologies with flexible partitioning, the increased encoding complexity has become a challenging issue in practical market usage. To address the complexity issue of VVC/H.266, significant efforts have been expended to develop practical methods for reducing the encoding and decoding processes of VVC/H.266. In this study, we provide an overview of the VVC/H.266 standard, and compared with previous video coding standards, examine a key challenge to VVC/H.266 coding. Furthermore, we survey and present recent technical advances in fast and low-complexity VVC/H.266, focusing on key technical areas.