This paper presents a comprehensive review of the current research on QCD axions, focusing on their potential as a solution to the strong CP problem and as a candidate for cold dark matter. Through detailed Monte Carlo simulations, the distribution of axion masses and couplings is explored, revealing critical insights into the likelihood of various parameter values. The study also examines the role of higher-order corrections in the axion potential, which significantly influence the dynamics of axions in the early universe. Furthermore, the paper discusses the potential of ultralight axions as quintessence, offering an intriguing link between axion physics and the accelerated expansion of the universe. The detection prospects for axions through their coupling with photons are analyzed, with a focus on experimental approaches such as ADMX and CAST. Finally, the results from a recent study on axion physics within the framework of string theory are incorporated, providing a broader context for understanding the cosmological implications of axions. The findings underscore the importance of refining axion models and experimental techniques to enhance the understanding of these elusive particles.