Magnetic monopoles were first proposed to exist by Dirac many decades ago as the natural counterparts of electrically charged particles such as the electron. Despite much searching, no elementary monopoles have ever been observed, even though many theories of high-energy physics suggest that they should be present. Here, we present an alternative route for the observation of monopoles as a low- rather than a high-energy phenomenon. It involves a process known as fractionalization, which is a striking emergent phenomenon, in which an 'elementary' particle breaks up into two independent entities. A celebrated example of this is spin-charge separation, in which an electron's magnetic spin and electric (charge) properties appear to become independent degrees of freedom. The spin ice materials Dy2Ti2O7 and Ho2Ti2O7 provide a rare instance of fractionalization in three dimensions: their atomic magnetic dipole moments fractionalize, resulting in elementary excitations which can be thought of as magnetic monopoles. This colloquium presents a self-contained introduction to theoretical concepts and experimental phenomena in the physics of spin ice. It focuses on the unique signatures of the peculiar nature of its ground state and its excitations. These include unusual neutron scattering structure factors, rich non-equilibrium physics, as well as a response to external magnetic fields that promotes spin ice as a magnetic Coulomb liquid, a magnetic analogue of an electrolyte. Finally, this talk addresses open questions and future perspectives for detecting individual monopoles, among them a (thought) experiment inspired by high energy physics.