Artificial neural networks are used in many stateof-the-art systems for perception, and they thrive at solving classification problems, but they lack the ability to transfer that learning to a new task. Human and animals both have the capability of acquiring knowledge and transfer them continually throughout their lifespan. This term is known as continual learning. Continual learning capabilities are important to ANN in the real world especially with the continuous stream of big data. However, it remains a challenge to be achieved because they are prone to a problem called catastrophic forgetting.. Fixing this problem is critical, so that ANN incrementally learn and improve when deployed to real life situations. In this paper, we did a taxonomy of continual learning in human by introducing plasticity-stability dilemma, hence the Hebbian plasticity and compensatory homeostatic plasticity process of learning and memory formation that occurs in the brain. We also did a state-of-the-art review of three different approaches to continual learning to mitigate catastrophic forgetting.