Reconfigurable intelligent surfaces (RIS) is regarded as a key enabler for future wireless communication systems. Recently, beyond-diagonal RIS (BD-RIS) has been proposed as an innovative generalization of conventional RIS, offering greater design flexibility and improved performance by adding connections between RIS elements. However, the increased number of connections also leads to high circuit complexity, posing a significant practical challenge. In this talk, we focus on the optimization and design of low-complexity BD-RIS architectures. We consider a BD-RIS aided multiuser multi-input single-output (MISO) system and model the BD-RIS architecture using graph theory. The formulated problems are solved by a custom-designed partially proximal alternating direction method of multipliers (pp-ADMM) algorithm. The pp-ADMM algorithm is computationally efficient, with each subproblem admitting a closed-form solution. In addition, we propose a new BD-RIS architectures that achieve the same flexibility of fully-connected RIS while maintaining low circuit complexity. The number of connections in the proposed architecture class is O(NK), where N and K denote the number of RIS elements and users, respectively, which is significantly lower than the O(N^2) complexity of fully-connected RIS (since K is much less than N in practice).