Person re-identification stands as a vibrant and actively researched domain within the computer vision community, due to its real-world applications and considerable research significance. In person re-identification, the unsupervised domain adaptation methods are an important topic of research which is alternatively referred as cross-domain adaptation. The lack of human identity information in deployable environments necessitates domain adaptation-based techniques that utilize a labeled sample from the source domain to learn the distinguishing features and further apply this knowledge to the unlabeled target domain. This work meticulously conducts a comparative analysis of state-of-the-art UDA methods, employing robust metrics such as the Cumulative Match Characteristics curve and mean Average Precision across prevalent re-identification datasets. Going beyond a mere survey, the paper systematically categorizes and evaluates the strengths and limitations of specific UDA methodologies, shedding light on their nuanced applications and potential challenges. Significantly, the review extends its scope to explore future research directions, emphasizing the critical role of hybrid approaches, integration with generative models, heterogeneous domain adaptation, and active learning. By providing an extensive resource for both researchers and practitioners, this paper not only offers insights into the current landscape of UDA in person re-identification but also contributes to the ongoing advancement of methods tailored for the complexities of dynamic and diverse real-world scenarios.