Presented by Akagi and coauthors in 1983, instantaneous reactive power theory (IRP theory) features low computational complexity and fast dynamic response, but it is not directly applicable to single-phase circuits. Scholars have been developing new approaches to define reactive power in single-phase circuits by utilizing the idea of IRP theory, i.e., mapping the voltage and current signals to a two-dimensional space with α-β transformation. This paper presents an overview of the reactive power definitions in single-phase circuits that are particularly based on IRP theory. Specifically, 3 types of definition are summarized: generalized instantaneous reactive power theory, reactive current theory, and instantaneous reactive power density theory. Furthermore, the current applications and the constraints of these theories are discussed in detail.