Nonlinear transmission lines (NLTLs) have been increasingly studied to produce high power microwaves (HPM) at higher repetition rates than conventional HPM devices without requiring the same auxiliary systems. The ability to array NLTLs to produce higher power and achieve beam steering provides an additional capability. This review summarizes the various NLTL topologies designed to achieve these design objectives. Specifically, we summarize modeling and experimental studies for three primary topologies: the lumped element NLTL, the split ring resonator, and the traditional transmission line geometry using nonlinear materials. The lumped element NLTL and the traditional transmission line constructed with nonlinear materials lend themselves to higher power applications, while the split ring resonator is better suited for applications involving antennas. We provide a detailed summary of past studies for these topologies and conclude by exploring ongoing work and future opportunities for technological development.