Due to aging infrastructure, technical issues, increased demand, and environmental developments, the reliability of power systems is of paramount importance. Utility companies aim to provide uninterrupted and efficient power supply to their customers. To achieve this, they focus on implementing techniques and methods to minimize downtime in power networks and reduce maintenance costs. In addition to traditional statistical methods, modern technologies such as machine learning have become increasingly common for enhancing system reliability and customer satisfaction. The primary objective of this study is to review parametric and nonparametric machine learning techniques and their applications in relation to maintenance-related aspects of power distribution system assets, including (1) distribution lines, (2) transformers, and (3) insulators. Compared to other reviews, this study offers a unique perspective on machine learning algorithms and their predictive capabilities in relation to the critical components of power distribution systems.