Axion-Like Particles (ALPs) are ubiquitous in String Theory compactifications that could describe our world. Their coupling to electromagnetism leads to a rich phenomenology, in particular in astrophysical environments. X-ray data on galaxy clusters and active galactic nuclei allows to constrain the properties of ALPs and/or give hints for new physics, including dark matter. The talk will be based on https://arxiv.org/abs/1605.01043 and https://arxiv.org/abs/1608.01684.