During working memory tasks, the firing rates of single neurons recorded in behaving monkeys remain elevated without external cues. Modeling studies have explored different mechanisms that could underlie this selective persistent activity, including recurrent excitation within cell assemblies, synfire chains and single-cell bistability. The models show how sustained activity can be stable in the presence of noise and distractors, how different synaptic and voltage-gated conductances contribute to persistent activity, how neuromodulation could influence its robustness, how completely novel items could be maintained, and how continuous attractor states might be achieved. More work is needed to address the full repertoire of neural dynamics observed during working memory tasks.