Humans and animals learn throughout life. Such continual learning is crucial for intelligence. In this chapter, we examine the pivotal role plasticity mechanisms with complex internal synaptic dynamics could play in enabling this ability in neural networks. By surveying theoretical research, we highlight two fundamental enablers for continual learning. First, synaptic plasticity mechanisms must maintain and evolve an internal state over several behaviorally relevant timescales. Second, plasticity algorithms must leverage the internal state to intelligently regulate plasticity at individual synapses to facilitate the seamless integration of new memories while avoiding detrimental interference with existing ones. Our chapter covers successful applications of these principles to deep neural networks and underscores the significance of synaptic metaplasticity in sustaining continual learning capabilities. Finally, we outline avenues for further research to understand the brain's superb continual learning abilities and harness similar mechanisms for artificial intelligence systems.