Recent neurophysiological studies in awake, behaving primates have revealed that neurons in certain brain areas appear to integrate sensory evidence over time during the performance of perceptual decision-making tasks. Neurons in the lateral intraparietal area (LIP) of rhesus monkeys exhibit such decision-related signals while the animals view and judge the direction of a visual motion display. Further investigation of this temporal integration process using brief perturbations of the sensory evidence has suggested that LIP neurons do not integrate evidence in a perfect, linear manner. We describe how a biophysically-plausible attractor network model can account for many aspects of the temporal dynamics of neural activity during these perceptual decisions. We also review a larger set of models and explain how the dynamics during and after temporal integration can help to distinguish the underlying neural mechanisms. Finally, we propose some crucial theoretically-motivated experiments that are needed to test among models.