The goal of our project is the determination of bound states and resonances emerging from the theory of the strong interaction, Quantum Chromodynamics (QCD), within the Standard Model of Particle Physics. In the last two decades, many states with properties not well-described by the naive quark model picture of quark-antiquark mesons and three-quark baryons have been observed. A particular focus of our project are mesons with a heavy charm or bottom quark, some of which seem to have a large four-quark component, suggestive of meson-meson bound states. To study these states we employ a discretized version of QCD referred to as Lattice QCD, along with Effective Field Theory (EFT methods).