Crime linkage is the process of analyzing criminal behavior data to determine whether a pair or group of crime cases are connected or belong to a series of offenses. This domain has been extensively studied by researchers in sociology, psychology, and statistics. More recently, it has drawn interest from computer scientists, especially with advances in artificial intelligence. Despite this, the literature indicates that work in this latter discipline is still in its early stages. This study aims to understand the challenges faced by machine learning approaches in crime linkage and to support foundational knowledge for future data-driven methods. To achieve this goal, we conducted a comprehensive survey of the main literature on the topic and developed a general framework for crime linkage processes, thoroughly describing each step. Our goal was to unify insights from diverse fields into a shared terminology to enhance the research landscape for those intrigued by this subject.