Photons are excellent carriers of quantum information. The generation, manipulation and read-out of photonic quantum states have enabled pioneering investigations in quantum physics, paving the way to groundbreaking technologies. Integrated quantum photonics, that is the processing of photons on-chip, is at the forefront of this revolution. In particular, silicon integrated circuits have emerged as the dominant material platform for large-scale quantum photonics. However, the difficulty to inject single photons on-demand in a silicon chip is a major obstacle to the level of complexity of current systems. In this context, the isolation of individual fluorescent defects in silicon, called color centers, opens an avenue toward the integration of atomic sources of single photons. While several color centers have demonstrated an ability to generate antibunched photons, practical applications require tailoring of their emission through quantum electrodynamics effects in optical cavities. This PhD thesis is devoted to cavity quantum electrodynamics with color centers in silicon optical cavities, in view of building an efficient source of single photons. The efforts are first focused on ensembles of G centers in microring cavities. The optical properties of cavity-coupled G centers are studied using microphotoluminescence spectroscopy, and an enhancement of their zero-phonon emission rate by Purcell effect is demonstrated. However, a quantitative analysis reveals a poor quantum efficiency, motivating the choice of another emitter for further experiments. Subsequently, the efforts are focused on the W center. Purcell enhancement of the overall recombination rate is observed for an ensemble of W centers in a circular Bragg grating cavity. Using a quantitative analysis based on finite-difference time-domain calculation, a high quantum efficiency is estimated. The results being encouraging for the purpose of single photon emission, an optical setup is developed for single-emitter spectroscopy and a strategy is devised to fabricate individually-adressable emitters, leading to the isolation of single W centers in unpatterned silicon-on-insulator. Using a nanofabrication process allowing for deterministic positionning, the emitters are embedded into circular Bragg grating cavities, resulting in an increase of the photoluminescence intensity by orders of magnitude by Purcell effect. This work leads to the demonstration of a source of triggered single photons. A next milestone will be the demonstration of a single photon source for integrated photonic circuits, based on a color center in a waveguide-coupled optical cavity. Beyond the interest for integrated quantum photonics, the observation of bright photoluminescence from single color centers opens perspectives for further experiments, allowing to probe fundamental questions relative to their photophysics.