The study of brain age has emerged over the past decade, aiming to estimate a person's age based on brain imaging scans. Ideally, predicted brain age should match chronological age in healthy individuals. However, brain structure and function change in the presence of brain-related diseases. Consequently, brain age also changes in affected individuals, making the brain age gap (BAG)-the difference between brain age and chronological age-a potential biomarker for brain health, early screening, and identifying age-related cognitive decline and disorders. With the recent successes of artificial intelligence in healthcare, it is essential to track the latest advancements and highlight promising directions. This review paper presents recent machine learning techniques used in brain age estimation (BAE) studies. Typically, BAE models involve developing a machine learning regression model to capture age-related variations in brain structure from imaging scans of healthy individuals and automatically predict brain age for new subjects. The process also involves estimating BAG as a measure of brain health. While we discuss recent clinical applications of BAE methods, we also review studies of biological age that can be integrated into BAE research. Finally, we point out the current limitations of BAE's studies.