This paper provides a comprehensive review of the use of computational bioacoustics as well as signal and speech processing techniques in the analysis of primate vocal communication. We explore the potential implications of machine learning and deep learning methods, from the use of simple supervised algorithms to more recent self‐supervised models, for processing and analyzing large data sets obtained within the emergence of passive acoustic monitoring approaches. In addition, we discuss the importance of automated primate vocalization analysis in tackling essential questions on animal communication and highlighting the role of comparative linguistics in bioacoustic research. We also examine the challenges associated with data collection and annotation and provide insights into potential solutions. Overall, this review paper runs through a set of common or innovative perspectives and applications of machine learning for primate vocal communication analysis and outlines opportunities for future research in this rapidly developing field.