Integrated photonics is emerging as a key technology for use in quantum information and communication. Driven by classical communication, which already has a swathe of scalable, efficient, and robust components, integrated photonics promises to transfer quantum science from a mere lab curiosity into a commercial reality. Chip-based quantum light sources are increasingly being recognized as a practical and high-performance alternative to bulky and power-hungry, table-top photon-pair sources. In particular, photon-pair sources based on spontaneous four-wave mixing in microring resonators (MRR) have emerged as a viable integrated photonic solution for quantum information and communication. This thesis relies on silicon nitride (Si3N4) MRR to realize narrowband, telecom photonpair sources. High quality factor MRRs are enabled by the low propagation losses in the Si3N4 platform; in this thesis, they are exploited to realize bright photon-pair sources with heralded spectral purity up to 0.98. Low quality factor MRRs are exploited for a proof-of-concept high-rate sequential time-bin entanglement with net visibilities up to 99.96 ± 0.03 %. For the goal of practical, real-world deployment of integrated photon-pair sources, it is not enough to demonstrate the performance of a single source. One also needs to demonstrate their high-performance operation in complex quantum networking protocols, such as entanglement swapping between genuinely independent sources. Here, for the first time, we demonstrate entanglement swapping between two independent, spatially separated, and asynchronously-pumped MRR photon-pair sources. Our sources operate in the continuous-wave regime, and time-resolved detection results in high Hong-Ou-Mandel (93.2 ±1.6 %) and entanglement swapping (91.2 ± 3.4 %) visibilities. Finally, to further improve our rates while maintaining high visibilities in multi-source interference scenarios, the origin of an on-chip-generated noise must be identified and mitigated. Here, we present our first efforts in the quest for tackling this notorious noise problem.