I will discuss some recent progress in studying hadrons using first-principles lattice QCD calculations. The spectroscopy and interactions of hadrons probe the strongly-interacting regime of QCD, and in recent years experiments have observed a number of puzzling hadrons that challenge our understanding of the strong interaction. Lattice QCD provides a method for performing first-principles computations of the properties of hadrons and hence a QCD-based understanding of the phenomena. However, the majority of hadrons decay strongly, i.e. they are resonances, and lattice calculations of these are challenging. I will present a selection of recent work that has advanced our understanding of hadrons including results relevant for the exotic doubly-charmed Tcc(3875) observed by LHCb, scalar and tensor charmonium resonances, and the D*0(2300) and enigmatic D*s0(2317) charm mesons.