Epicardial and pericardial adipose tissues (EAT and PAT), which are located around the heart, have been linked to coronary atherosclerosis, cardiomyopathy, coronary artery disease, and other cardiovascular diseases. Additionally, the volume and thickness of EAT are good predictors of CVD risk levels. Manual quantification of these tissues is a tedious and error-prone process. This paper presents a comprehensive and critical overview of research on the epicardial and pericardial adipose tissue segmentation and quantification methods, evaluates their effectiveness in terms of segmentation time and accuracy, provides a critical comparison of the methods, and presents ongoing and future challenges in the field. Described methods are classified into pericardial adipose tissue segmentation, direct epicardial adipose tissue segmentation, and epicardial adipose tissue segmentation via pericardium delineation. A comprehensive categorization of the underlying methods is conducted with insights into their evolution from traditional image processing methods to recent deep learning-based methods. The paper also provides an overview of the research on the clinical significance of epicardial and pericardial adipose tissues as well as the terminology and definitions used in the medical literature.