This article explores issues that govern the admissibility of Artificial Intelligence (“AI”) applications in civil and criminal cases, from the perspective of a federal trial judge and two computer scientists, one of whom also is an experienced attorney. It provides a detailed yet intelligible discussion of what AI is and how it works, a history of its development, and a description of the wide variety of functions that it is designed to accomplish, stressing that AI applications are ubiquitous, both in the private and public sectors. Applications today include: health care, education, employment-related decision-making, finance, law enforcement, and the legal profession. The article underscores the importance of determining the validity of an AI application (i.e., how accurately the AI measures, classifies, or predicts what it is designed to), as well as its reliability (i.e., the consistency with which the AI produces accurate results when applied to the same or substantially similar circumstances), in deciding whether it should be admitted into evidence in civil and criminal cases. The article further discusses factors that can affect the validity and reliability of AI evidence, including bias of various types, “function creep,” lack of transparency and explainability, and the sufficiency of the objective testing of AI applications before they are released for public use. The article next provides an in-depth discussion of the evidentiary principles that govern whether AI evidence should be admitted in court cases, a topic which, at present, is not the subject of comprehensive analysis in decisional law. The focus of this discussion is on providing a step-by-step analysis of the most important issues, and the factors that affect decisions on whether to admit AI evidence. Finally, the article concludes with a discussion of practical suggestions intended to assist lawyers and judges as they are called upon to introduce, object to, or decide on whether to admit AI evidence.