The main goal of the spectroscopy program at COMPASS is to explore the light-meson spectrum in the mass range below about 2 GeV/c 2 using diffractive dissociation reactions. Our flagship channel is the production of three charged pions in the reaction: π − + p → π − π − π + + p recoil , for which COMPASS has acquired the so far world's largest dataset of roughly 50 M exclusive events using an 190 GeV/c π − beam. Based on this dataset, we performed an extensive partial-wave analysis. In order to extract the parameters of the π J and a J resonances that appear in the π − π − π + system, we performed the so far most comprehensive resonance-model fit, using Breit-Wigner parametrizations. This method in combination with the high statistical precision of our data allows us to study ground and excited states. We study the a 4 (2040) resonance in the ρ(770)πG and f 2 (1270)πF decays. In addition to the ground state resonance a 1 (1260), we have found evidence for the a 1 (1640), which is the first excitations of the a 1 (1260), in our data. We also study the spectrum of π 2 states by simultaneously describing four J PC = 2 −+ waves using three π 2 resonances, the π 2 (1670), the π 2 (1880), and the π 2 (2005). Using a novel analysis approach, where the resonance-model fit is performed simultaneously in narrow bins of the squared four-momentum transfer t between the beam pion and the target proton, allows us to study the t dependence of resonant and non-resonant components included in our model. We observe that for most of the partial waves, the non-resonant components show a steeper t spectrum compared to the resonances and that the t spectrum of most of the resonances becomes shallower with increasing resonance mass. We also study the t dependence of the relative phases between resonance components. The pattern we observe is consistent with a common production mechanism of these states.