We present an end-to-end, two-phase model for the origin of globular clusters (GCs). In the model, populations of stellar clusters form in the high-pressure discs of high-redshift ($z>2$) galaxies (a rapid-disruption phase due to tidal perturbations from the dense interstellar medium), after which the galaxy mergers associated with hierarchical galaxy formation redistribute the surviving, massive clusters into the galaxy haloes, where they remain until the present day (a slow-disruption phase due to tidal evaporation). The high galaxy merger rates of $z>2$ galaxies allow these clusters to be `liberated into the galaxy haloes before they are disrupted within the high-density discs. This physically-motivated toy model is the first to include the rapid-disruption phase, which is shown to be essential for simultaneously reproducing the wide variety of properties of observed GC systems, such as their universal characteristic mass-scale, the dependence of the specific frequency on metallicity and galaxy mass, the GC system mass-halo mass relation, the constant number of GCs per unit supermassive black hole mass, and the colour bimodality of GC systems. The model predicts that most of these observables were already in place at $z=1$-$2$, although under rare circumstances GCs may still form in present-day galaxies. In addition, the model provides important constraints on models for multiple stellar populations in GCs by putting limits on initial GC masses and the amount of pristine gas accretion. The paper is concluded with a discussion of these and several other predictions and implications, as well as the main open questions in the field.
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