This paper presents a unified framework for the modeling, analysis, and design of load-independent Class E and Class EF inverters and rectifiers. These circuits are able to maintain zero-voltage switching and, hence, high efficiency for a wide load range without requiring tuning or use of a feedback loop, and to simultaneously achieve a constant amplitude ac voltage or current in inversion and a constant dc output voltage or current in rectification. As switching frequencies are gradually stepping into the megahertz (MHz) region with the use of wide-bandgap (WBG) devices such as GaN and SiC, switching loss, implementing fast control loops, and current sensing become a challenge, which load-independent operation is able to address, thus allowing exploitation of the high-frequency capability of WBG devices. The traditional Class E and EF topologies are first presented, and the conditions for load-independent operation are derived mathematically; then, a thorough analytical characterization of the circuit performance is carried out in terms of voltage and current stresses and the power-output capability. From this, design contours and tables are presented to enable the rapid implementation of these converters given particular power and load requirements. Three different design examples are used to showcase the capability of these converters in typical MHz power conversion applications using the design equations and methods presented in this paper. The design examples are chosen toward enabling efficient and high-power-density MHz converters for wireless power transfer (WPT) applications and dc/dc conversion. Specifically, a 150-W 13.56-MHz Class EF inverter for WPT, a 150-W 10-MHz miniature Class E boost converter, and a lightweight wirelessly powered drone using a 20-W 13.56-MHz Class E synchronous rectifier have been designed and are presented here.