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Perovskite solar cells (PSCs) have attracted much attention because of their rapid rise to 22% efficiencies. Here, we review the rapid evolution of PSCs as they enter a new phase that could revolutionize the photovoltaic industry. In particular, we describe the properties that make perovskites so remarkable, and the current understanding of the PSC device physics, including the operation of state-of-the-art solar cells with efficiencies above 20%. The extraordinary progress of long-term stability is discussed and we provide an outlook on what the future of PSCs might soon bring the photovoltaic community. Some challenges remain in terms of reducing non-radiative recombination and increasing conductivity of the different device layers, and these will be discussed in depth in this review.