Low-power edge and IoT devices are increasingly expected to operate autonomously in energy-constrained environments, while maintaining reliable sensing, computation, and communication over long lifetimes. This tutorial provides a circuit- and system-level overview of power management techniques that enable such devices, with emphasis on two representative application domains. The first part focuses on energy harvesting for battery-assisted or battery-less IoT sensor nodes, particularly piezoelectric energy harvesting. Key challenges include extracting energy efficiently from weak and highly variable transducers, achieving cold start and maximum power point operation, managing intermittent power availability, and delivering regulated supply voltages to ultra-low-power loads. The second part addresses inductive wireless power transfer for biomedical implants, where power delivery must meet stringent requirements on size, efficiency, safety, and reliability. Topics include resonant inductive links, AC–DC rectification, voltage regulation, load-adaptive power management, and system constraints imposed by implantable applications.