Recent progress on hadron spectroscopy from lattice QCD

Lattice QCD has matured to a degree where it is now possible to study excited hadrons as they truly appear in nature, as short-lived resonant enhancements decaying into multiple possible final states. Through variational analysis of matrices of correlation functions computed with large bases of interpolating fields it has proven possible to extract many excited state energy levels, and these can be used to constrain the hadron-hadron scattering amplitudes in which hadron resonances can be observed. Recent progress is illustrated with several examples including coupled-channel scattering in the $\pi \eta, K\overline{K}$ and $\pi\pi, K\overline{K}, \eta\eta$ systems in which the $a_0, f_0$ scalar mesons appear.