Exciton-polaritons are hybrid light-matter quasi-particles formed by the strong coupling of excitons (electron-hole pairs) and cavity photons in a semiconductor microcavity. They can form Bose-Einstein condensates (BEC) that are inherently non-equilibrium in nature due to the very short polariton lifetime and coexist with an incoherent reservoir of excitons feeding the condensate. These introduces additional decoherence mechanisms that can directly affect the long-range coherence in this system. In this seminar, I will present my works in understanding the formation of coherence and the influence of the reservoir. First, I will discuss the time-evolution of the formation of spatial coherence of an optically trapped polariton condensate in the pulsed regime, where we uncover transient oscillations of the first-order correlation function in space and time. Second, I will focus on discussing the role of spatial overlap of the reservoir and the condensate on the temporal coherence in the steady-state regime by measuring the polariton emission linewidth. We demonstrate the robustness of the polariton condensate’s coherence properties against reservoir-condensate overlap if the condensate is sufficiently trapped and the excitation is significantly above threshold. Finally, we report the realization of a highly coherent polariton laser with ultra-narrow linewidths ten times narrower than previous reports