The widespread availability of high-performance computing and the popularity of artificial intelligence (AI) with machine learning and deep learning (ML/DL) algorithms at the helm have stimulated the development of many applications involving the use of AI-based techniques in molecular imaging research. Applications reported in the literature encompass various areas, including innovative design concepts in positron emission tomography (PET) instrumentation, quantitative image reconstruction and analysis techniques, computer-aided detection and diagnosis, as well as modeling and prediction of outcomes. This review reflects the tremendous interest in quantitative molecular imaging using ML/DL techniques during the past decade, ranging from the basic principles of ML/DL techniques to the various steps required for obtaining quantitatively accurate PET data, including algorithms used to denoise or correct for physical degrading factors as well as to quantify tracer uptake and metabolic tumor volume for treatment monitoring or radiation therapy treatment planning and response prediction.This review also addresses future opportunities and current challenges facing the adoption of ML/DL approaches and their role in multimodality imaging.