The growing interest in axion-like particles (ALPs) stems from the fact that they provide successful theoretical explanations of physics phenomena, from the anomaly of the CP-symmetry conservation in strong interactions to the observation of an unexpectedly large TeV photon flux from astrophysical sources, at distances where the strong absorption by the intergalactic medium should make the signal very dim. In this latter condition, which is the focus of this review, a possible explanation is that TeV photons convert to ALPs in the presence of strong and/or extended magnetic fields, such as those in the core of galaxy clusters or around compact objects, or even those in the intergalactic space. This mixing affects the observed γ-ray spectrum of distant sources, either by signal recovery or the production of irregularities in the spectrum, called ‘wiggles’, according to the specific microscopic realization of the ALP and the ambient magnetic field at the source, and in the Milky Way, where ALPs may be converted back to γ rays. ALPs are also proposed as candidate particles for the Dark Matter. Imaging Atmospheric Cherenkov telescopes (IACTs) have the potential to detect the imprint of ALPs in the TeV spectrum from several classes of sources. In this contribution, we present the ALP case and review the past decade of searches for ALPs with this class of instruments.