A traffic monitoring system is an integral part of Intelligent Transportation Systems (ITS). It is one of the critical transportation infrastructures that transportation agencies invest a huge amount of money to collect and analyze the traffic data to better utilize the roadway systems, improve the safety of transportation, and establish future transportation plans. With recent advances in MEMS, machine learning, and wireless communication technologies, numerous innovative traffic monitoring systems have been developed. In this article, we present a review of state-of-the-art traffic monitoring systems focusing on the major functionality-vehicle classification. We organize various vehicle classification systems, examine research issues and technical challenges, and discuss hardware/software design, deployment experience, and system performance of the vehicle classification systems. Finally, we discuss a number of critical open problems and future research directions in an aim to provide valuable resources to academia, industry, and government agencies for selecting appropriate technologies for their traffic monitoring applications.