Understanding the excited spectrum of hadrons from first
principles remains a challenging prospect. The majority of excited hadrons
are seen as resonances in the scattering of lighter stable hadrons like
pions and kaons. Many resonances decay into multiple final states
necessitating coupled-channel analyses, and recently it has become
possible to obtain coupled-channel scattering amplitudes from lattice QCD.
I will describe the methods used in these calculations, to first compute
large spectra, that are then used to constrain scattering t-matrices, from
which the complex resonance poles can be extracted. Several recent
applications of these methods will be described, including the first
extraction of a strongly-coupled scattering amplitude from QCD where an a0
resonance was found in coupled-channel pi-eta K-Kbar scattering.