Bandit problems provide an interesting and widely-used setting for the study of sequential decision-making. In their most basic form, bandit problems require people to choose repeatedly between a small number of alternatives, each of which has an unknown rate of providing reward. We investigate restless bandit problems, where the distributions of reward rates for the alternatives change over time. This dynamic environment encourages the decision-maker to cycle between states of exploration and exploitation. In one environment we consider, the changes occur at discrete, but hidden, time points. In a second environment, changes occur gradually across time. Decision data were collected from people in each environment. Individuals varied substantially in overall performance and the degree to which they switched between alternatives. We modeled human performance in the restless bandit tasks with two particle filter models: one that can approximate the optimal solution to a discrete restless bandit problem, and another simpler particle filter that is more psychologically plausible. It was found that the simple particle filter was able to account for most of the individual differences. (This work was funded by award FA95500710082 from the Air Force Office of Scientific Research.)