Fifty years after the discovery of QCD experimental and theoretical efforts continue to uncover structures in its spectrum - sometimes unexpectedly. In the heavy sector alone, for example, among the about 62 (LHCb'22) new hadron states observed, many are 4- or 5-quark states. These states are phenomenologically difficult to explain and conclusions are often contradictory depending on how QCD interactions are modelled. In this talk I will present current efforts to resolve parts of this impasse by performing QCD calculations without approximation using advanced lattice techniques. Focussing on doubly heavy tetraquarks, recent lattice calculations will be reviewed and paths towards understanding the substructure of these states sketched out. To illustrate I will give details on the possibility of understanding deeply bound doubly heavy tetraquarks in terms of diquark effective degrees of freedom and how the properties of these diquarks can be determined on the lattice.