The paper addresses the implementation of stacked intelligent metasurfaces (SIMs) using beyond diagonal reconfigurable intelligent surfaces (BD-RIS) and derives a physically consistent channel model for SIM-aided systems. The authors first derive a general channel model that accounts for mutual coupling effects at the transmitter, SIM layers, and receiver, using multiport network theory. They then simplify this model to a form commonly used in recent literature, clarifying the assumptions required for this simplification. The study compares SIM architectures implemented with diagonal RIS (D-RIS) and BD-RIS, showing that a 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity, while any $L$-layer SIM implemented with D-RIS is suboptimal. Numerical results support these theoretical findings, demonstrating that 1-layer SIMs based on BD-RIS outperform those based on D-RIS in terms of channel gain and circuit complexity. The paper concludes by discussing future research directions, including the impact of assumptions on the channel model, optimization of SIM in more general systems, and prototyping of SIM.The paper addresses the implementation of stacked intelligent metasurfaces (SIMs) using beyond diagonal reconfigurable intelligent surfaces (BD-RIS) and derives a physically consistent channel model for SIM-aided systems. The authors first derive a general channel model that accounts for mutual coupling effects at the transmitter, SIM layers, and receiver, using multiport network theory. They then simplify this model to a form commonly used in recent literature, clarifying the assumptions required for this simplification. The study compares SIM architectures implemented with diagonal RIS (D-RIS) and BD-RIS, showing that a 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity, while any $L$-layer SIM implemented with D-RIS is suboptimal. Numerical results support these theoretical findings, demonstrating that 1-layer SIMs based on BD-RIS outperform those based on D-RIS in terms of channel gain and circuit complexity. The paper concludes by discussing future research directions, including the impact of assumptions on the channel model, optimization of SIM in more general systems, and prototyping of SIM.