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Efficient wireless power transfer across tissue is highly desirable for removing bulky energy storage components. Most existing power transfer systems are conceptually based on coils linked by slowly varying magnetic fields (less than 10 MHz). These systems have many important capabilities, but are poorly suited for tiny, millimeter-scale implants where extreme asymmetry between the source and the receiver results in weak coupling. This paper first surveys the analysis of near-field power transfer and associated strategies to optimize efficiency. It then reviews analytical models that show that significantly higher efficiencies can be obtained in the electromagnetic midfield. The performance limits of such systems are explored through optimization of the source, and a numerical example of a cardiac implant demonstrates that millimeter-sized devices are feasible.