The axion arises in well-motivated extensions of the Standard Model of particle physics and is regarded as an alternative to the weakly interacting massive particle paradigm to explain the nature of dark matter. In this contribution, we review theoretical aspects of dark matter axions, particularly focusing on recent developments in the estimation of their relic abundance. A closer look at their non-thermal production mechanisms in the early universe reveals the possibility of explaining the observed dark matter abundance in various mass ranges. The mass ranges predicted in various cosmological scenarios are briefly summarized.