This work addresses recent developments for solving problems in process systems engineering based on machine learning algorithms. A general description of most popular supervised and unsupervised learning algorithms is presented, as well as the applications addressed in the current literature. Because of their wide usage and potential applications, support vector machines and neural networks are addressed as special cases. The approach used is fundamentally didactic. Therefore, several of the references included are recommendations for novice readers interested in entering the area of machine learning and data science. The applications were selected considering simplicity, popularity of the application, and accessibility for inexperienced readers, but with knowledge of the process systems engineering area. Finally, a critical perspective for future development and applications is provided. Epistemological issues and modeling limitations are discussed in order to analyze the real significance of data-driven strategies as well as a questioning of academic marketing in recent years.