The advent of social media platforms presented unprecedented opportunities in sharing information, real-time communication and virtual collaborations. However, social media platforms have been used maliciously and subsequently lead to cyberbullying. Detecting cyberbullying manually is almost impossible due to massive data generated by social media users daily. Several strategies including opinion mining methods, machine learning techniques and deleting fake profiles have been utilized to deal with cyberbullying on social media platforms. However, due to the nature and structure of datasets as well as the language used, it is tremendously becoming difficult to detect cyberbullying. Therefore, this study presents a comprehensive review of deep learning models applied to detect cyberbullying on various social media platforms. Among deep learning models, convolutional neural networks, long short-term memory (LSTM), bidirectional LSTM, recurrent neural networks and bidirectional gated recurrent unit are predominantly used to detect different forms of cyberbullying such as hate speech, harassment, sexism, bullying among others. The study also revealed that cyberbullying causes psychological effects such as stress, anxiety, worthlessness, depression, reduced self-esteem, suicidal ideation and psychological distress, frustration, sleep-related issues and psychosis. This study also revealed that the majority of deep learning-based cyberbullying detection models utilized Twitter textual dataset. In the future, there is a need to utilize multimedia data such as images, audio and videos from various social media platforms to effectively develop cyberbullying detection models that can automatically detect all forms of bullying. This can tremendously assist law enforcement agencies to curb the menace of cyberbullying on various social media platforms.