ABSTRACT Starburst (SB) galaxies are a rare population of galaxies with star formation rates (SFRs) greatly exceeding those of the majority of star-forming galaxies with similar stellar mass. It is unclear whether these bursts are the result of either especially large gas reservoirs or enhanced efficiencies in converting gas into stars. Tidal torques resulting from gas-rich galaxy mergers are known to enhance the SFR by funnelling gas towards the centre. However, recent theoretical works show that mergers do not always trigger an SB and not all SB galaxies are interacting systems, raising the question of what drives an SB. We analyse a large sample of SB galaxies and a mass- and redshift-matched sample of control galaxies, drawn from the FIREbox cosmological volume at z = 0–1. We find that SB galaxies have both larger molecular gas fractions and shorter molecular depletion times than control galaxies, but similar total gas masses. Control galaxies evolve towards the SB regime by gas compaction in their central regions, over time-scales of ∼70 Myr, accompanied by an increase in the fraction of ultradense and molecular gas. The driving mechanism behind the SB varies depending on the mass of the galaxy. Massive ($M_⋆ \gtrsim 10^{10}~\rm {M}_⊙$) galaxies undergoing intense, long-lasting SBs are mostly driven by galaxy interactions. Conversely, SBs in non-interacting galaxies are often triggered by a global gravitational instability, which can result in a ‘breathing’ mode in low-mass galaxies.