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Artificial agents interacting in highly dynamic environments are required to continually acquire and fine-tune their knowledge overtime. In contrast to conventional deep neural networks that typically rely on a large batch of annotated training samples, lifelong learning systems must account for situations in which the number of tasks is not known a priori and the data samples become incrementally available over time. Despite recent advances in deep learning, lifelong machine learning has remained a long-standing challenge due to neural networks being prone to catastrophic forgetting, i.e., the learning of new tasks interferes with previously learned ones and leads to abrupt disruptions of performance. Recently proposed deep supervised and reinforcement learning models for addressing catastrophic forgetting suffer from flexibility, robustness, and scalability issues with respect to biological systems. In this tutorial, we will present and discuss well-established and emerging neural network approaches motivated by lifelong learning factors in biological systems such as neurosynaptic plasticity, complementary memory systems, multi-task transfer learning, and intrinsically motivated exploration.