We combine constraints on the galaxy–dark matter connection with structural and dynamical scaling relations to investigate the angular momentum content of disc galaxies. For haloes with masses in the interval 1011.3 M⊙≲Mvir≲ 1012.7 M⊙ we find that the galaxy spin parameters are basically independent of halo mass with . This is significantly lower than for relaxed Λcold dark matter (ΛCDM) haloes, which have an average spin parameter . The average ratio between the specific angular momentum of disc galaxies and their host dark matter haloes is therefore . This calls into question a standard assumption made in the majority of all (semi-analytical) models for (disc) galaxy formation, namely that . Using simple disc formation models we show that it is particularly challenging to understand why is independent of halo mass, while the galaxy formation efficiency (εGF; proportional to the ratio of galaxy mass to halo mass) reveals a strong halo mass dependence. We argue that the empirical scaling relations between εGF, and halo mass require both feedback (i.e. galactic outflows) and angular momentum transfer from the baryons to the dark matter (i.e. dynamical friction). Most importantly, the efficiency of angular momentum loss needs to decrease with increasing halo mass. Such a mass dependence may reflect a bias against forming stable discs in high-mass, low-spin haloes or a transition from cold-mode accretion in low-mass haloes to hot-mode accretion at the massive end. However, current hydrodynamical simulations of galaxy formation, which should include these processes, seem unable to reproduce the empirical relation between εGF and . We conclude that the angular momentum build-up of galactic discs remains poorly understood.