Two-dimensional hexagonal boron nitride (2D-hBN) is an emerging 2D material that has received considerable attention due to its exceptional properties including electric insulation, low dielectric constant, easy synthesis, high-temperature stability, corrosion resistance, and chemical stability. 2D-hBN can be integrated with other 2D materials such as graphene in the next generation of electronic and optoelectronic devices and van der Waals heterostructures. In this review, unique properties of the 2D-hBN are discussed, and recent advancements in the synthesis methods such as mechanical exfoliation, liquid exfoliation, ion intercalation, chemical vapor deposition, physical vapor deposition, magnetron sputtering, pulsed laser deposition, ion sputtering deposition, and some more techniques are reviewed. Furthermore, versatile applications of 2D-hBN nanosheets in graphene electronics, tunneling barrier, dielectrics, passivation layers, deep ultraviolet light sources, single-photon emitters, sensors, and catalysis are critically analyzed. Current challenges and future perspectives for the utilization of 2D-hBN in the next-generation ultrathin electronic devices are discussed.