Short-range wireless power and data transmission offers a viable mean to power up implantable medical devices (IMDs) with a wide range of power levels and communicate with external units across the skin. To optimize wireless power transfer (WPT), it is key to improve efficiencies in every stage of the power delivery path from external power sources to the IMD, while maintaining robustness and safety against load variations, coil misalignments, and nearby conductive objects. This paper reviews various mechanisms for WPT with focus on link structures and circuit techniques for wirelessly-powered IMDs. Moreover, advanced IMDs require wireless data telemetry (WDT) for wideband bidirectional data communication in the presence of the strong power carrier interference. This paper also discusses several modulation schemes and transceiver circuits for low-power, carrier-less, and robust WDT.