<p>It has been 50 years since thermodynamics and general relativity were united in the study of black-hole thermodynamics. This Review covers the established principles in the subject, including the four laws of black-hole thermodynamics, notions of temperature and entropy, and the chemical behaviour exhibited by black holes. However, there are still many unsolved puzzles in black-hole thermodynamics: we discuss violations of the third law, non-equilibrium behaviour and black-hole microstructure, as well as the information paradox that encapsulates a deep conundrum between gravitation and quantum physics. We also assess the prospects for progress through understanding multicritical behaviour and the dynamics of phase changes, the use of holographic approaches, and, ultimately, the resolution of the information paradox. After 50 years, black-hole thermodynamics still offers much to learn about the relationship between gravitation and quantum physics.</p>