Majority-inverter graphs (MIGs) are a multi-level logic representation of Boolean functions with remarkable algebraic and Boolean properties that enable efficient logic optimizations beyond the capabilities of conventional logic representations. In this paper, we survey two state-of-the-art logic optimization methods for MIGs: cut rewriting and cut resubstitution. Both algorithms are generic and can be applied to arbitrary graph-based logic representations. We describe them in a unified framework and show experimental results for MIG size optimization using the EPFL combinational benchmark suite.