Visual short-term memory (VSTM) is thought to help bridge across changes in visual input, and yet many studies of VSTM employ static displays. Here we investigate how VSTM copes with sequential input. In particular, we characterize the temporal dynamics of several different components of VSTM performance, including: storage probability, precision, variability in precision, guessing, and swapping. We used a variant of the continuous-report VSTM task developed for static displays, quantifying the contribution of each component with statistical likelihood estimation, as a function of serial position and set size. In Experiments 1 and 2, storage probability did not vary by serial position for small set sizes, but showed a small primacy effect and a robust recency effect for larger set sizes; precision did not vary by serial position or set size. In Experiment 3, the recency effect was shown to reflect an increased likelihood of swapping out items from earlier serial positions and swapping in later items, rather than an increased rate of guessing for earlier items. Indeed, a model that incorporated responding to non-targets provided a better fit to these data than alternative models that did not allow for swapping or that tried to account for variable precision. These findings suggest that VSTM is updated in a first-in-first-out manner, and they bring VSTM research into closer alignment with classical working memory research that focuses on sequential behavior and interference effects.