Single-photon sources and their optical spin readout are at the core of applications in quantum communication, quantum computation, and quantum sensing. Their integration in photonic structures such as photonic crystals, microdisks, microring resonators, and nanopillars is essential for their deployment in quantum technologies. While there are currently only two material platforms (diamond and silicon carbide) with proven single-photon emission from the visible to infrared, a quantum spin–photon interface, and ancilla qubits, it is expected that other material platforms could emerge with similar characteristics in the near future. These two materials also naturally lead to monolithic integrated photonics as both are good photonic materials. While so far the verification of single-photon sources was based on discovery, assignment and then assessment and control of their quantum properties for applications, a better approach could be to identify applications and then search for the material that could address the requirements of the application in terms of quantum properties of the defects. This approach is quite difficult as it is based mostly on the reliability of modeling and predicting of color center properties in various materials, and their experimental verification is challenging. In this paper, we review some recent advances in an emerging material, low-dimensional (2D, 1D, 0D) hexagonal boron nitride (h-BN), which could lead to establishing such a platform. We highlight the recent achievements of the specific material for the expected applications in quantum technologies, indicating complementary outstanding properties compared to the other 3D bulk materials.