Artificial intelligence (AI) is the development of computer systems that are able to perform tasks that normally require human intelligence. Advances in AI software and hardware, especially deep learning algorithms and the graphics processing units (GPUs) that power their training, have led to a recent and rapidly increasing interest in medical AI applications. In clinical diagnostics, AI-based computer vision approaches are poised to revolutionize image-based diagnostics, while other AI subtypes have begun to show similar promise in various diagnostic modalities. In some areas, such as clinical genomics, a specific type of AI algorithm known as deep learning is used to process large and complex genomic datasets. In this review, we first summarize the main classes of problems that AI systems are well suited to solve and describe the clinical diagnostic tasks that benefit from these solutions. Next, we focus on emerging methods for specific tasks in clinical genomics, including variant calling, genome annotation and variant classification, and phenotype-to-genotype correspondence. Finally, we end with a discussion on the future potential of AI in individualized medicine applications, especially for risk prediction in common complex diseases, and the challenges, limitations, and biases that must be carefully addressed for the successful deployment of AI in medical applications, particularly those utilizing human genetics and genomics data.