Throughout the past several decades, mobile devices have evolved in capability and popularity at growing rates while improvement in security has fallen behind. As smartphones now hold mass quantities of sensitive information from millions of people around the world, addressing this gap in security is crucial. Recently, researchers have experimented with behavioral and physiological biometrics-based authentication to improve mobile device security. Continuing the previous work in this field, this study identifies popular dynamics in behavioral and physiological smartphone authentication and aims to provide a comprehensive review of their performance with various deep learning and machine learning algorithms. We found that utilizing hybrid schemes with deep learning features and deep learning/machine learning classification can improve authentication performance. Throughout this paper, the benefits, limitations, and recommendations for future work will be discussed.