Lifelong Machine Learning (LML) is a versatile improvement to neural networks that in- creases models’ ability to learn from sequential data in bite size and incrementally, while continually expanding generally acquired knowledge to new tasks. One of the persistent problems encountered in LML is known as catastrophic forgetting, whereby nets dislearn prior tasks upon exposure to new tasks. The following review explores these challenges in detail and presents fundamental neural network-based approaches to address such troubles in lifelong learning systems. In the edition, we prevent updates some of the key connectivist parameters while retaining prior knowledge from other tasks through regularization methods such as Elastic Weight Consolidation (EWC) and Learning without Forgetting (LwF). Even though useful, such strategies should be used with caution since they require as much emphasis on revisiting previous tasks as on acquiring new ones. Other rehearsal methods include the Partition Reservoir Sampling (PRS) and Optimizing Class Distribution in Memory (OCDM) that uses a portion of previous data for retraining, which can however prove rather space consuming for large-scale applications. Some architectural approaches, like the Compact, Picking, and Growing (CPG) principle, mean that the network structure grows with new tasks and extend from existing neurons or layers without influence from previous information. But these methods predetermine scalability since they increase computational complexity with the size of a casual network. Nevertheless, problems of how to deal with imbalance in data and shift in labels are still open problems particularly when applied in situations where the data distribution changes over time. However, lifelong learning in neural networks continue to experience growth challenges in catastrophic forgetting, scalability, and efficient knowledge transfer thus the need for further re-search. It will be crucial for applying neural networks for situations where it is required to learn over time but do not want to forget what has been learnt earlier.