ABSTRACT We use the simba cosmological galaxy formation simulation to investigate the relationship between major mergers ($\lesssim$4:1), starbursts, and galaxy quenching. Mergers are identified via sudden jumps in stellar mass M* well above that expected from in situ star formation, while quenching is defined as going from specific star formation rate (sSFR) $\gt t_{\rm H}^{-1}$ to $\lt 0.2t_{\rm H}^{-1}$, where tH is the Hubble time. At z ≈ 0–3, mergers show ∼2–3× higher SFR than a mass-matched sample of star-forming galaxies, but globally represent $\lesssim 1{{\ \rm per\ cent}}$ of the cosmic SF budget. At low masses, the increase in SFR in mergers is mostly attributed to an increase in the H2 content, but for $M_*\gtrsim 10^{10.5} \,\mathrm{ M}_{⊙ }$ mergers also show an elevated star formation efficiency suggesting denser gas within merging galaxies. The merger rate for star-forming galaxies shows a rapid increase with redshift, ∝(1 + z)3.5, but the quenching rate evolves much more slowly, ∝(1 + z)0.9; there are insufficient mergers to explain the quenching rate at $z\lesssim 1.5$. simba first quenches galaxies at $z\gtrsim 3$, with a number density in good agreement with observations. The quenching time-scales τq are strongly bimodal, with ‘slow’ quenchings (τq ∼ 0.1tH) dominating overall, but ‘fast’ quenchings (τq ∼ 0.01tH) dominating in M* ∼ 1010–1010.5 M$⊙$ galaxies, likely induced by simba’s jet-mode black hole feedback. The delay time distribution between mergers and quenching events suggests no physical connection to either fast or slow quenching. Hence, simba predicts that major mergers induce starbursts, but are unrelated to quenching in either fast or slow mode.