Hexagonal boron nitride (hBN) has emerged as a key two-dimensional material. Its importance is linked to that of graphene because it provides an ideal substrate for graphene with minimal lattice mismatch and maintains its high carrier mobility. Moreover, hBN has unique properties in the deep ultraviolet (DUV) and infrared (IR) wavelength bands owing to its indirect bandgap structure and hyperbolic phonon polaritons (HPPs). This review examines the physical properties and applications of hBN-based photonic devices that operate in these bands. A brief background on BN is provided, and the theoretical background of the intrinsic nature of the indirect bandgap structure and HPPs is discussed. Subsequently, the development of DUV-based light-emitting diodes and photodetectors based on hBN’s bandgap in the DUV wavelength band is reviewed. Thereafter, IR absorbers/emitters, hyperlenses, and surface-enhanced IR absorption microscopy applications using HPPs in the IR wavelength band are examined. Finally, future challenges related to hBN fabrication using chemical vapor deposition and techniques for transferring hBN to a substrate are discussed. Emerging techniques to control HPPs are also examined. This review is intended to assist researchers in both industry and academia in the design and development of unique hBN-based photonic devices operating in the DUV and IR wavelength regions.