The increasing access to health data worldwide is driving a resurgence in machine learning research, including data-hungry deep learning algorithms. More computationally efficient algorithms now offer unique opportunities to enhance diagnosis, risk stratification, and individualised approaches to patient management. Such opportunities are particularly relevant for the management of older patients, a group that is characterised by complex multimorbidity patterns and significant interindividual variability in homeostatic capacity, organ function, and response to treatment. Clinical tools that utilise machine learning algorithms to determine the optimal choice of treatment are slowly gaining the necessary approval from governing bodies and being implemented into healthcare, with significant implications for virtually all medical disciplines during the next phase of digital medicine. Beyond obtaining regulatory approval, a crucial element in implementing these tools is the trust and support of the people that use them. In this context, an increased understanding by clinicians of artificial intelligence and machine learning algorithms provides an appreciation of the possible benefits, risks, and uncertainties, and improves the chances for successful adoption. This review provides a broad taxonomy of machine learning algorithms, followed by a more detailed description of each algorithm class, their purpose and capabilities, and examples of their applications, particularly in geriatric medicine. Additional focus is given on the clinical implications and challenges involved in relying on devices with reduced interpretability and the progress made in counteracting the latter via the development of explainable machine learning.