There is a growing body of research focusing on automatic detection of ischemia and myocardial infarction (MI) using computer algorithms. In clinical settings, ischemia and MI are diagnosed using electrocardiogram (ECG) recordings as well as medical context including patient symptoms, medical history, and risk factors-information that is often stored in the electronic health records. The ECG signal is inspected to identify changes in the morphology such as ST-segment deviation and T-wave changes. Some of the proposed methods compute similar features automatically while others use nonconventional features such as wavelet coefficients. This review provides an overview of the methods that have been proposed in this area, focusing on their historical evolution, the publicly available datasets that they have used to evaluate their performance, and the details of their algorithms for ECG and EHR analysis. The validation strategies that have been used to evaluate the performance of the proposed methods are also presented. Finally, the paper provides recommendations for future research to address the shortcomings of the currently existing methods and practical considerations to make the proposed technical solutions applicable in clinical practice.