The diversity of research on visual attention and multiple-object tracking presents challenges for anyone hoping to develop a unified account. One key challenge is identifying the attentional limitations that give rise to competition among targets during tracking. To address this challenge, we present a computational model of object tracking that relies on two attentional mechanisms: serial selection and parallel enhancement. Selection picks out an object for further processing, whereas enhancement increases sensitivity to stimuli in regions where objects have been selected previously. In this model, multiple target locations can be tracked in parallel via enhancement, whereas a single target can be selected so that additional information beyond its location can be processed. In simulations of two psychological experiments, we demonstrate that spatial competition during enhancement and temporal competition for selection can explain a range of findings on multiple-object tracking, and we argue that the interaction between selection and enhancement captured in the model is critical to understanding attention more broadly.