Wireless powered communication (WPC) is an emerging paradigm where wireless devices are powered over the air while exchanging information with them. This technology is attractive for various wireless applications, including classical radio-frequency identification (RFID) systems, implantable sensors, environmental sensing as found in agriculture and forestry, and simultaneous charging and telemetry communications for electric vehicles. While recent studies have shown that inductive coupling provides a more energy-efficient and robust channel for short and middle-range wireless transmission, most of the previous analyses on WPC have been limited to far-field transmission models. To this end, this work provides a comprehensive framework to design and analyze WPC over inductively coupled circuits. We consider three problems, namely, wireless power transfer (WPT), simultaneous wireless information and power transfer (SWIPT), and wireless powered communication network (WPCN) using multiple coupled coils. Each configuration is modeled by an abstract circuit model in which various effects, including mutual coupling and parasitic elements, are captured by a small number of measurable parameters. This technique allows us to not only eliminate the need for solving the circuit but also apply well-known signal processing techniques such as beamforming and channel estimation to inductively coupled models. For each of the three models, we derive the properties of the optimal source signal. In addition, we propose methods to design the load impedance of WPCN by taking into account the nonlinear effects due to impedance mismatches in the circuits.