The very outer solar atmosphere (corona) is very hot with temperatures over a million degrees K, while the photosphere is of the order of 5000 K. Embedded in this hot outer corona are cool, ≤10,000 K, magnetic structures called solar prominences. As seen on the disk, they are long filamentary structures while on the solar limb they look like intricate loops. In this paper, we present the development of our understanding of solar prominences, which have played a central role in the development of solar science. Solar prominences were first observed during the few minute episodes of total eclipses. The introduction of spectroscopy allowed continuous observations, which also led to information on temperatures, temporal variations and dynamics of the associated plasma. The discovery of strong magnetic fields in sunspots provided a breakthrough in our understanding of the physics of the Sun. Weaker magnetic fields formed both the large and small-scale structures of prominences, their time-variable shapes, and explained why they could remain floating high above the solar surface in the less dense corona. Appearing as dark, thin, elongated filaments against a brighter solar disk, they provided further information through their interaction with and dependence on how magnetic fields are distributed on the solar surface, in the chromosphere and corona. Access to X-ray and short-wavelength ultraviolet radiation in prominences from spacecraft revealed large ranges of temperature in thin layers between the 10,000-degree prominence cores and the surrounding million-degree corona. The advent of increasingly more powerful computers has led to advanced modelling of prominence plasma based on radiative transfer and magnetohydrodynamic (MHD) calculations. Theoretical and observational progress has opened up new possible formation mechanisms. The spectacular eruptions of solar prominences have led to a considerable amount of observational and theoretical work on possibly similar events on other stars, which could affect the existence of life on their orbiting planets.