"Quantum coherent phenomena, especially marcoscopic quantum coherence, are among the most striking predictions of quantum mechanics. They have lead to remarkable applications such as lasers and modern optical technologies, and in the future, breakthroughs such as quantum information processing are envisioned. Macroscopic quantum coherence is manifested in Bose-Einstein condensation (BEC), superfluidity, and superconductivity, which have been observed in a variety of systems and continue to be at the front line of scientific research. Here my objective is to extend the realm of Bose-Einstein condensation into new conceptual and practical directions. I focus on the role of a hybrid character of the object that condenses and on the role of non-equilibrium in the BEC phenomenon. The work is mostly theoretical but has also an experimental part. I study two new types of hybrids, fundamentally different from each other. First, I consider pairing and superfluidity in a mixed geometry. Experimental realization of mixed geometries is becoming feasible in ultracold gases. Second, I explore the possibility of finding novel hybrids of light and matter excitations that may display condensation. By combining insight from these two cases, my goal is to understand how the hybrid and non-equilibrium nature can be exploited to design desirable properties, such as high critical temperatures. In particular, in case of the new light-matter hybrids, the goal is to provide realistic scenarios for, and also experimentally demonstrate, a room temperature BEC."