Description In recent years, the spectroscopy of hadrons containing heavy quarks has brought forward a plethora of new and unexpected resonance-like signals. Many of these so-called $X$, $Y$,$Z$ states are candidates for states beyond the quark-antiquark configurations of mesons, which have been sought after since the introduction of the quark model. Similar studies in the light-quark sector are more challenging due to the wide and overlapping nature of known resonances. Recent high-quality data samples, collected by the COMPASS experiment at CERN, open the possibility to search for exotics also at masses below 2.5 GeV. In particular, hadrons with explicit gluonic degrees of freedom are expected in this mass region. Recently, lattice QCD started to make predictions on the multiplet structure of these so-called hybrid states, which may be used as a guideline in the experimental searches. The COMPASS experiment at CERN uses a high-energy pion beam scattered off protons and heavier nuclei to produce mesonic excitations, which are observed in multi-particle final states subjected to partial-wave analyses. In addition to studying the properties of established mesons with unprecedented accuracy, the large existing data samples allow us to detect possibly exotic states. These either do not fit current theoretical expectations, like the recently observed $a_1(1420)$, or carry spin-exotic quantum numbers, like the $\pi_1(1600)$. The talk will give an overview of ongoing studies of these states involving novel analysis techniques and discuss possible interpretations. Future plans concerning hadron spectroscopy in the strange and charm quark sector, envisaged at AMBER/COMPASS++, a new fixed-target QCD facility at CERN, will be presented.