This review introduces axions as a dark matter candidate, focusing on their cosmological implications relevant to current searches. It covers early-Universe production mechanisms, axion mass predictions, cosmological bounds on axion properties, and both direct and indirect detection methods for relic axions. The review discusses axion-like particles as dark matter, cosmological constraints on QCD and ultralight axions, and various detection techniques such as axion decay, stimulated decay, conversion, birefringence, and direct detection. It also addresses the role of axions in dark matter models, their production scenarios, and the observational signatures they leave in astrophysical data. The review emphasizes the importance of cosmology in guiding experimental searches for axions and highlights the significance of axions in understanding dark matter and the early Universe. It concludes with a discussion of the current state of axion cosmology and the challenges in confirming axions as dark matter.This review introduces axions as a dark matter candidate, focusing on their cosmological implications relevant to current searches. It covers early-Universe production mechanisms, axion mass predictions, cosmological bounds on axion properties, and both direct and indirect detection methods for relic axions. The review discusses axion-like particles as dark matter, cosmological constraints on QCD and ultralight axions, and various detection techniques such as axion decay, stimulated decay, conversion, birefringence, and direct detection. It also addresses the role of axions in dark matter models, their production scenarios, and the observational signatures they leave in astrophysical data. The review emphasizes the importance of cosmology in guiding experimental searches for axions and highlights the significance of axions in understanding dark matter and the early Universe. It concludes with a discussion of the current state of axion cosmology and the challenges in confirming axions as dark matter.