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Résumé : Axions comprise a broad class of particles that can play a major role in explaining the unknown aspects of cosmology. They are also extraordinarily well-motivated within high energy physics, and so axion cosmology offers us a unique view onto these theories. I present a comprehensive and pedagogical view on the cosmology and astrophysics of axion-like particles, starting from inflation and progressing via the CMB and structure formation up to the present-day Universe. I briefly review the motivation and models for axions in particle physics and string theory. The primary focus is on the population of ultralight axions created via vacuum realignment, and its role as a dark matter (DM) candidate with distinctive phenomenology. Cosmological observations place robust constraints on the axion mass and relic density in this scenario, and I review where such constraints come from. I next cover aspects of galaxy formation with axion DM, and ways this can be used to further search for evidence of axions. An absolute lower bound on DM particle mass is established. It is $m_a>10^{-24}\text{ eV}$ from linear observables, extending to $m_a\gtrsim 10^{-22}\text{ eV}$ from non-linear observables, and has the potential to reach $m_a\gtrsim 10^{-18}\text{ eV}$ in the future. I then spend some time discussing direct and indirect detection of axions, reviewing existing and future experiments. Miscellaneous additional topics covered include: axions as dark radiation, and axions as dark energy; decays of heavy axions; axions and stellar astrophysics; black hole superradiance; axions and astrophysical magnetic fields; axion inflation, and axion DM as an indirect probe of inflation.