The advancement in the computational capability and storage size of a modern mobile device has evolved it into a multi-purpose smart device for individual and business needs. The increasing usage of this device has led to the need for a secure and efficient authentication mechanism. For securing mobile devices, password, PIN, and swipe patterns are commonly used for user authentication. Entry-point face and fingerprint recognition have also gained traction in the past years. However, these authentication schemes cannot authenticate a user after the initial-login session. This limitation might put the device exposed to information theft and leakage if an illegitimate user could bypass the initial-login session. Therefore, a mobile device needs a continuous authentication mechanism that can protect a user throughout the entire working session, which complements the initial-login authentication to provide more comprehensive security protection. Touch biometric is a behavioural biometric that represents the touch behaviour pattern of a user when interacting with the touchscreen of the device. Touch biometric has been proposed as a continuous authentication mechanism, where the device can collect touch biometric data transparently while a user is using the device. However, there are still plenty of challenges and obstacles in touch-based continuous mobile device authentication due to its challenges as a biometric modality. This paper provides a comprehensive overview of fundamental principles that underpin touch-based continuous mobile device authentication. Our work discusses state-of-the-art methods in touch data acquisition, behavioural feature extraction, user classification, and evaluation methods. This paper also discusses some challenges and opportunities in the current touch-based continuous mobile device authentication domain to obtain a broad research community and market acceptance.