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Online continual learning (OCL) refers to the ability of a system to learn over time from a continuous stream of data without having to revisit previously encountered training samples. Learning continually in a single data pass is crucial for agents and robots operating in changing environments and required to acquire, fine-tune, and transfer increasingly complex representations from non-i.i.d. input distributions. Machine learning models that address OCL must alleviate \textit{catastrophic forgetting} in which hidden representations are disrupted or completely overwritten when learning from streams of novel input. In this chapter, we summarize and discuss recent deep learning models that address OCL on sequential input through the use (and combination) of synaptic regularization, structural plasticity, and experience replay. Different implementations of replay have been proposed that alleviate catastrophic forgetting in connectionists architectures via the re-occurrence of (latent representations of) input sequences and that functionally resemble mechanisms of hippocampal replay in the mammalian brain. Empirical evidence shows that architectures endowed with experience replay typically outperform architectures without in (online) incremental learning tasks.