This paper presents a literature review on magnetically-controlled devices, variable inductors (VI), and variable transformers (VT), and their applications to lighting gears for discharge lamps and/or LED lamps. These current-controlled devices are mainly characterized by nonlinear and non-uniform saturation of the magnetic core. The paper describes the fundamentals and basic operating principle of such devices and provides an overview of existing patents. These patents refer the devices, VIs or VTs, as useful or industrially applicable. Some present one or more claims regarding the construction of the device and behavioral characteristic; others refer to specific applications, such as voltage regulation or universal ballast operation. Afterwards, the paper focuses on the review of specific techniques and circuits taking advantage of the presence of a controlled inductance value, by covering recent applications regarding discharge and solid-state lamp drivers. These applications will show how these multi-winding devices, typically not considered due to their low efficiency, may fulfill an important role and add features to state-of-the-art lamp drivers.