This review discusses the development of quantum light sources using flat optics, particularly metasurfaces. Quantum light sources are essential for quantum technologies, enabling secure communication, powerful computing, and precise sensing. Recent advancements have shifted towards using "flat" optics with subwavelength thickness for quantum light sources, offering advantages over bulky counterparts in compactness, scalability, and efficiency. The review covers the generation of entangled photon pairs through spontaneous parametric down-conversion in nonlinear metasurfaces and single photon emission from quantum emitters like quantum dots and color centers in 2D materials. It discusses theoretical principles, fabrication techniques, and properties of these sources, emphasizing enhanced generation and engineering of quantum light sources using optical resonances supported by nanostructures. The review also highlights the diverse applications of these sources and current challenges in the field. Metasurfaces, composed of nanostructured materials, enable precise control of light properties such as polarization, wavefront, and spectral characteristics. They can enhance light-matter interactions and provide multifunctional control of optical waves. The review discusses the generation of quantum entangled photon pairs from nonlinear flat-optics, including the use of nonlinear nanoresonators and metasurfaces for producing polarization-entangled photons. It also covers the generation of complex quantum states in spatial, spectral, and polarization degrees of freedom using metasurfaces. Flat optics have been used to develop solid-state single photon emitters (SPEs) such as quantum dots and color centers in 2D materials. These SPEs can generate deterministic single photons and are enhanced by photonic structures that increase the photon radiative rate, route photons into desired modes, and add additional degrees of freedom. The review discusses the use of metasurfaces to control the emission properties of SPEs, including polarization, direction, and orbital angular momentum. The review also addresses challenges and future prospects in the development of quantum light sources using flat optics. These include improving the efficiency and coherence of quantum light sources, enhancing the generation of entangled photons, and developing compact, high-performance photon sources. The integration of metasurfaces with SPEs and other quantum emitters is highlighted as a promising direction for future research. The review concludes that the combination of flat optics and quantum light sources is a rapidly growing field with significant potential for advancements in quantum technologies.This review discusses the development of quantum light sources using flat optics, particularly metasurfaces. Quantum light sources are essential for quantum technologies, enabling secure communication, powerful computing, and precise sensing. Recent advancements have shifted towards using "flat" optics with subwavelength thickness for quantum light sources, offering advantages over bulky counterparts in compactness, scalability, and efficiency. The review covers the generation of entangled photon pairs through spontaneous parametric down-conversion in nonlinear metasurfaces and single photon emission from quantum emitters like quantum dots and color centers in 2D materials. It discusses theoretical principles, fabrication techniques, and properties of these sources, emphasizing enhanced generation and engineering of quantum light sources using optical resonances supported by nanostructures. The review also highlights the diverse applications of these sources and current challenges in the field. Metasurfaces, composed of nanostructured materials, enable precise control of light properties such as polarization, wavefront, and spectral characteristics. They can enhance light-matter interactions and provide multifunctional control of optical waves. The review discusses the generation of quantum entangled photon pairs from nonlinear flat-optics, including the use of nonlinear nanoresonators and metasurfaces for producing polarization-entangled photons. It also covers the generation of complex quantum states in spatial, spectral, and polarization degrees of freedom using metasurfaces. Flat optics have been used to develop solid-state single photon emitters (SPEs) such as quantum dots and color centers in 2D materials. These SPEs can generate deterministic single photons and are enhanced by photonic structures that increase the photon radiative rate, route photons into desired modes, and add additional degrees of freedom. The review discusses the use of metasurfaces to control the emission properties of SPEs, including polarization, direction, and orbital angular momentum. The review also addresses challenges and future prospects in the development of quantum light sources using flat optics. These include improving the efficiency and coherence of quantum light sources, enhancing the generation of entangled photons, and developing compact, high-performance photon sources. The integration of metasurfaces with SPEs and other quantum emitters is highlighted as a promising direction for future research. The review concludes that the combination of flat optics and quantum light sources is a rapidly growing field with significant potential for advancements in quantum technologies.