In this presentation, I would like to discuss some promising schemes of heralded sources of single photons and photon pairs based on spontaneous four-wave mixing (SFWM) and third-order spontaneous parametric down-conversion (TOSPDC), respectively, in ring microresonators. In the first case, the optimal design for an integrated SFWM-based single-photon source, which consists of a system of coupled ring microresonators and provides the highest purity of generated photons is developed. In the second case, it is shown that silicon-nitride based microresonators are promising systems for observing TOSPDC. In particular, the phase-matching condition for degenerate TOSPDC can be attained simultaneously with the zero group velocity dispersion for the triphoton field. Under such conditions, nondegenerate TOSPDC is possible, thereby allowing to produce frequency entangled three-photon states and heralded frequency entangled two-photon states.