ABSTRACT We present a detailed analysis of the physical processes that cause halo assembly bias – the dependence of halo clustering on proxies of halo formation time. We focus on the origin of assembly bias in the mass range corresponding to the hosts of typical galaxies and use halo concentration as our chief proxy of halo formation time. We also repeat our key analyses across a broad range of halo masses and for alternative formation time definitions. We show that splashback subhaloes are responsible for two-thirds of the assembly bias signal, but do not account for the entire effect. After splashback subhaloes have been removed, we find that the remaining assembly bias signal is due to a relatively small fraction ($\lesssim \!10{{\ \rm per\ cent}}$) of haloes in dense regions. We test a number of additional physical processes thought to contribute to assembly bias and demonstrate that the two key processes are the slowing of mass growth by large-scale tidal fields and by the high velocities of ambient matter in sheets and filaments. We also rule out several other proposed physical causes of halo assembly bias. Based on our results, we argue that there are three processes that modify the assembly bias of small-mass haloes arising from the properties of the primordial Gaussian field: large-scale tidal fields, gravitational heating due to the collapse of large-scale structures, and splashback subhaloes located outside the virial radius.