Young massive clusters (YMCs) are usually accompanied by lower-mass clusters and unbound stars with a total mass equal to several tens times the mass of the YMC. If this was also true when globular clusters (GCs) formed, then their cosmic density implies that most star formation before redshift ∼2 made a GC that lasted until today. Star-forming regions had to change after this time for the modern universe to be making very few YMCs. Here we consider the conditions needed for the formation of a ∼106 M o cluster. These include a star formation rate (SFR) inside each independent region that exceeds ∼1 M o yr-1 to sample the cluster mass function up to such a high mass, and an SFR per unit area of ΣSFR ∼ 1 M o kpc-2 yr-1 to get the required high gas surface density from the Kennicutt-Schmidt relation, and therefore the required high pressure from the weight of the gas. High pressures are implied by the virial theorem at cluster densities. The ratio of these two quantities gives the area of a GC-forming region, ∼1 kpc2, and the young stellar mass converted to a cloud mass gives a typical gas surface density of 500-1000 M o pc-2. Observations of star-forming clumps in young galaxies are consistent with these numbers, suggesting that they formed today's GCs. Observations of the cluster cutoff mass in local galaxies agree with the maximum mass calculated from ΣSFR. Metal-poor stellar populations in local dwarf irregular galaxies confirm the dominant role of GC formation in building their young disks.