Modern atom-optics experiments allow one an unprecedented control of atomic degrees of freedom and, as a consequence, the clean realization of toy models used to explain transport phenomena in condensed matter physics. We present recent results on extended Bose-Hubbard systems. For reasonable lattice sizes, this model gives access to the full quantum spectrum, which allows us a complete characterization of ``horizontal'' (spatially) and ``vertical'' (energetic) quantum transport. Various dynamical regimes can be prepared, using the atom-atom interactions, disorder, and external forces as control parameters. While for a disordered model we predict a crossover between quantum chaotic and localised dynamics, we show that the interband transport of atoms confined to a periodic lattice and subject to an additional tilting force is strongly dependent on the dynamics of the ground-state band. Since experiments are currently getting into the regime of small filling factors, we hope for an observation of our predictions showing the impact of disorder on quantum transport and of many-body interaction on Landau-Zener tunnelling.