The discovery of a multitude of new hadronic resonances in recent decades has spurred renewed theoretical interest in the field of hadron spectroscopy. For some of these states there is significant tension between the measurement and the expectation from quark models. Lattice QCD has established itself as a useful tool to study the hadron spectrum in a model-independent way. Using the Lüscher finite-volume formalism, lattice spectra can be used to constrain scattering amplitudes. In this talk I will review recent progress in the realm of open-charm systems. I will also discuss the computational challenges in applying the method to hadrons with a greater number of valence quarks, such as baryons and tetraquarks, and some ideas to overcome them.