In this talk we describe the DS approach to QCD and 3-dimensional QED. After sketching the formal derivation of the DSEs, we first consider the heavy quark limit of nonperturbative Coulomb gauge QCD and the confinement problem. In this framework, we demonstrate, under truncation, a direct connection between the Yang-Mills sector of the theory (the temporal component of the gluon propagator) and the quark confining potential. We further show that only color singlet quark-antiquark (meson) and three-quark (baryon) bound states are physically allowed, and discuss the implications for phenomenological studies of hadrons. Turning to QED3, we consider an infinite slab of graphene and investigate its properties in the setup of an effective quantum field theoretical model. Specifically, we study the gap generation, also in relation to the structural defects and transport properties of graphene. In particular, we show that breaking the sublattice symmetry in a graphene monolayer leads to confined states of massless Dirac fermions — experimentally, this corresponds to chemical bonding of foreign atoms to carbon atoms.