This article presents a comprehensive overview of recent advances in coupling matrix optimization and topology design methodologies for multiplexer synthesis. The study also explores channel frequency allocation schemes that may produce novel innovative multiplexer topologies. The article begins with a systematic overview of multiplexer synthesis and design through four procedural steps. Optimization based coupling matrix synthesis for all-resonator multiplexers is covered at length including both local and global synthesis methods. Novel multiplexer structures based on optimization synthesis are introduced with several synthesis examples and experimental evaluation.