In the course of the second quantum revolution, quantum mechanics is put to practice in novel quantum technologies like quantum information technology, quantum cryptography, or quantum computing. Non-classical states of light such as single photons or entangled photon pairs, that are at the heart of many fascinating applications in these fields, can be created in semiconductor quantum dot-cavity systems. This cumulative thesis theoretically investigates the possibility to generate and manipulate highly non-classical states of light in such systems. To this end, the influence of various system parameters, e.g., the energy of involved cavity modes, intrinsic electronic properties, or external optical excitation, is analyzed. Because quantum dots unavoidably interact with their semiconductor environment they are influenced by temperature-dependent lattice vibrations, i.e., phonons, which are known to have a profound impact, even at cryogenic temperatures. In order to assess the impact of longitudinal acoustic phonons on photonic figures of merit without any approximations to the microscopic description, a numerically complete path-integral approach is employed. This thesis presents a variety of notable results that may pave the way towards more advanced sources of non-classical states of light. Assuming an initially excited quantum dot, the impact of different quantum dot-cavity configurations and phonons on polarization-entangled photon pairs is studied, highlighting the importance of direct two-photon processes. In contrast to previous expectations, parameter areas are found for certain configurations, where a phonon-induced enhancement of photon entanglement takes place. The possibility to generate different types of entangled Bell states in continuously excited quantum emitter-cavity systems is discussed. Based on an in-depth numerical and analytic investigation of this system, a protocol realizing an active, time-dependent switching between different types of entanglement is proposed. In the case of strongly confined quantum dots, a phase transition-like behavior for photon pair states and the suppression of N-photon bundles due to the strong phonon impact in constantly driven systems is revealed. A profound phonon influence is also encountered during the investigation of shape-changing photon number distributions that emerge after the excitation with chirped laser pulses. Precisely timed and tailored laser pulses are employed to investigate the quality of single photons and store individual photons in a metastable dark exciton state. Quite remarkably, it is uncovered that the widely used quantum regression theorem systematically overestimates the phonon impact on the indistinguishability. As highlight of the work, it is demonstrated that the achievable degree of photon entanglement in state-of-the-art experiments is limited due to a Stark-shift introduced by the two-photon resonant excitation scheme. In total, this thesis gives detailed insights into the generation of non-classical states of light valuable to all working in photonic quantum technologies.