This article presents an extensive review of the state-of-the-art system-level solutions featuring complexity reduction and/or dedicated hardware designs for the AV1 and VVC video coding formats. These formats introduced several novel coding techniques compared to their predecessors to improve the coding efficiency at the cost of a significant computational cost. In this article, we discuss the main novelties of AV1 and VVC in each coding module, including block partitioning, intra and inter prediction, transform, entropy coding, and in-loop filters. Then, we present the main published works focusing on complexity reduction and hardware designs for AV1 and VVC. Most of the complexity reduction solutions target the complex and flexible block partitioning structures of these encoders to provide a better tradeoff between coding efficiency and complexity reduction whereas the hardware designs focus on the challenge of implementing the new coding tools to attend real-time processing of high-definition videos. Even with the presented works reaching impressive results, these research fields remain opened for innovative contributions, as discussed in this article.