With the rapid progress of big data and artificial intelligence, machine learning technologies such as learning and adaptive control have emerged as a research focus in petroleum engineering. They have various applications in oilfield development, such as parameter prediction, optimization scheme deployment, and performance evaluation. This paper provides a comprehensive review of these applications in three key scenarios of petroleum engineering, namely hydraulic fracturing and acidizing, chemical flooding and gas flooding, and water injection. This article first introduces the steps and methods of machine learning processing in these scenarios, then discusses the advantages, disadvantages, existing challenges, and future prospects of these machine learning methods. Furthermore, this article compares and contrasts the strengths and weaknesses of these machine learning methods, aiming to help researchers select and improve their methods. Finally, this paper identifies some potential development trends and research directions of machine learning in petroleum engineering based on the current issues.