  Quantum light sources are essential building blocks for many quantum
technologies, enabling secure communication, powerful computing, precise
sensing and imaging. Recent advancements have witnessed a significant shift
towards the utilization of ``flat" optics with thickness at subwavelength
scales for the development of quantum light sources. This approach offers
notable advantages over conventional bulky counterparts, including compactness,
scalability, and improved efficiency, along with added functionalities. This
review focuses on the recent advances in leveraging flat optics to generate
quantum light sources. Specifically, we explore the generation of entangled
photon pairs through spontaneous parametric down-conversion in nonlinear
metasurfaces, as well as single photon emission from quantum emitters including
quantum dots and color centers in 3D and 2D materials. The review covers
theoretical principles, fabrication techniques, and properties of these
sources, with particular emphasis on the enhanced generation and engineering of
quantum light sources using optical resonances supported by nanostructures. We
discuss the diverse application range of these sources and highlight the
current challenges and perspectives in the field.
