We use the EAGLE cosmological hydrodynamic simulation suite to study the specific angular momentum of galaxies, j, with the aims of (i) investigating the physical causes behind the wide range of j at fixed mass and (ii) examining whether simple, theoretical models can explain the seemingly complex and non-linear nature of the evolution of j. We find that j of the stars, j(stars), and baryons, j(bar), are strongly correlated with stellar and baryon mass, respectively, with the scatter being highly correlated with morphological proxies such as gas fraction, stellar concentration, (u-r) intrinsic colour, stellar age and the ratio of circular velocity to velocity dispersion. We compare with available observations at z = 0 and find excellent agreement. We find that j(bar) follows the theoretical expectation of an isothermal collapsing halo under conservation of specific angular momentum to within approximate to 50 per cent, while the subsample of rotation-supported galaxies are equally well described by a simple model in which the disc angular momentum is just enough to maintain marginally stable discs. We extracted evolutionary tracks of the stellar spin parameter of EAGLE galaxies and found that the fate of their j(stars) at z = 0 depends sensitively on their star formation and merger histories. From these tracks, we identified two distinct physical channels behind low j(stars) galaxies at z = 0: (i) galaxy mergers, and (ii) early star formation quenching. The latter can produce galaxies with low j(stars) and early-type morphologies even in the absence of mergers.