Globular clusters (GCs) are massive (mostly M>1e5 Msun), metal-poor (mostly sub-solar) and old (mostly > 10 Gyr) stellar clusters that have remained gravitationally bound till the present day. Their formation mechanism is heavily debated in the modern literature, but their old ages make them excellent probes of the conditions of the early Universe. I will review the hypothesis where GCs are the relics of regular cluster formation at high redshift that survived until z=0. To quantitatively address this hypothesis, I will present the E-MOSAICS project, a suite of 25 present day Milky Way-mass cosmological zoom-in simulations that enables the self-consistent study of the formation and co-evolution of stellar clusters and their host galaxies through cosmic time. I will discuss how a wide range of observables of cluster populations are reproduced in the simulations, such as the number of GCs per unit stellar mass and their radial distribution, and I will explain how we can use GC populations to reconstruct the merger history of the host galaxy, with applications to the Milky Way.