Recent research has shown the possibility of using smartphones' sensors and accessories to extract some behavioral attributes such as touch dynamics, keystroke dynamics and gait recognition. These attributes are known as behavioral biometrics and could be used to verify or identify users implicitly and continuously on smartphones. The authentication systems that have been built based on these behavioral biometric traits are known as active or continuous authentication systems. This paper provides a review of the active authentication systems. We present the components and the operating process of the active authentication systems in general, followed by an overview of the state-of-the-art behavioral biometric traits that used to develop an active authentication systems and their evaluation on smartphones. We discuss the issues, strengths and limitations that associated with each behavioral biometric trait. Also, we introduce a comparative summary between them. Finally, challenges and open research problems are presented in this research field.