Mass distribution of black holes in low-mass X-ray binaries previously suggested the existence of a ∼2–5 M⊙ mass gap between the most massive neutron stars and the least massive black holes, while some recent evidence appears to support that this mass gap is being populated. Whether there is a mass gap or not can potentially shed light on the physics of supernova explosions that form neutron stars and black holes, although significant mass accretion of neutron stars including binary mergers may lead to the formation of mass-gap objects. In this review, I collect the compact objects that are probable black holes with masses being in the gap. Most of them are in binaries, their mass measurements are obviously subject to some uncertainties. Current observations are still unable to confidently infer an absence or presence of the mass gap. Ongoing and future surveys are expected to build the mass spectrum of black holes which can be used to constrain the process of their formation especially in binaries. I describe the theoretical predictions for the formation of black holes in various types of binaries, and present some prospects of searching for black holes via electromagnetic and gravitational wave observations.