Power electronics are a key element in all kinds of systems and are important for addressing the world's energy challenges. This talk describes emerging approaches in the design of power electronics that seek to address the twin challenges of miniaturization and improved performance. Through architectures and topologies that minimize magnetic energy storage, the scaling limitations of magnetic components can be offset, leading to smaller, higher-performance power converters. One such approach is the use of hybrid switched-capacitor/magnetic conversion. To illustrate this, the talk describes a hybrid "multi-track" converter for telecom applications that provides a 5:1 input voltage range while achieving a power density of > 450 W/in3, over 3 times that of the best comparable commercial design. The use of greatly increased switching frequencies to provide miniaturization is also explored. We demonstrate this in the context of ac-dc converters for supplying low voltage from the grid, and show a prototype design operating in the 3-10 MHz range that achieves greatly improved power density as compared to conventional converters.