Impedance networks cover the entire of electric power conversion from dc (converter, rectifier), ac (inverter), to phase and frequency conversion (ac-ac) in a wide range of applications. Various converter topologies have been reported in the literature to overcome the limitations and problems of the traditional voltage source, current source as well as various classical buck-boost, unidirectional, and bidirectional converter topologies. Proper implementation of the impedance-source network with appropriate switching configurations and topologies reduces the number of power conversion stages in the system power chain, which may improve the reliability and performance of the power system. The first part of this paper provides a comprehensive review of the various impedance-source-networks-based power converters and discusses the main topologies from an application point of view. This review paper is the first of its kind with the aim of providing a 'one-stop' information source and a selection guide on impedance-source networks for power conversion for researchers, designers, and application engineers. A comprehensive review of various modeling, control, and modulation techniques for the impedance-source converters/inverters will be presented in Part II.