Semiconductor devices include a transistor having a gate structure located close to a channel region that comprises a colossal magnetocapacitive material. The gate structure is configured to affect electrical current flow through the channel region between a source and a drain. The colossal magnetocapacitive material optionally may be disposed between two structures, one or both of which may be electrically conductive, magnetic, or both electrically conductive and magnetic. Methods of fabricating semiconductor devices include forming a colossal magnetocapacitive material close to a channel region between a source and a drain of a transistor, and configuring the colossal magnetocapacitive material to exhibit colossal magnetocapacitance for generating an electrical field in the channel region. Methods of affecting current flow through a transistor include causing a colossal magnetocapacitive material to exhibit colossal magnetocapacitance and generate an electrical field in a channel region of a transistor.