ABSTRACT We use the SAMI Galaxy Survey to examine the drivers of galaxy spin, $λ _{R_{\rm e}}$, in a multidimensional parameter space including stellar mass, stellar population age (or specific star formation rate), and various environmental metrics (local density, halo mass, satellite versus central). Using a partial correlation analysis, we consistently find that age or specific star formation rate is the primary parameter correlating with spin. Light-weighted age and specific star formation rate are more strongly correlated with spin than mass-weighted age. In fact, across our sample, once the relation between light-weighted age and spin is accounted for, there is no significant residual correlation between spin and mass, or spin and environment. This result is strongly suggestive that the present-day environment only indirectly influences spin, via the removal of gas and star formation quenching. That is, environment affects age, then age affects spin. Older galaxies then have lower spin, either due to stars being born dynamically hotter at high redshift, or due to secular heating. Our results appear to rule out environmentally dependent dynamical heating (e.g. galaxy–galaxy interactions) being important, at least within 1 Re where our kinematic measurements are made. The picture is more complex when we only consider high-mass galaxies (M* ≳ 1011 M⊙). While the age-spin relation is still strong for these high-mass galaxies, there is a residual environmental trend with central galaxies preferentially having lower spin, compared to satellites of the same age and mass. We argue that this trend is likely due to central galaxies being a preferred location for mergers.