Eye tracking is widely used in developmental research to measure infants' looking behavior before, during, or after particular events and can provide a measure of real-time processing. However, the dynamic time course of infants' looking behaviors is rarely analyzed. Instead, eye tracking data is often averaged within a large window or is restricted to certain predictive or reactive looks before or after an event, which could conceal interesting looking patterns. In this article, we discuss an alternative approach using spline models -- an approachable and informative method for analyzing how the trajectory of infants' looking behaviors changes at discrete time points. We illustrate the benefits of spline models by demonstrating how to prepare, estimate, and interpret the results of a spline model in R and SAS, and we compare the results with an analysis of averaged looking times within a time window. We show that spline models can reveal patterns in the trajectory of participants' looking that can be obscured by averaged looking times. Finally, we use a sensitivity analysis to show that spline models are reliable with small samples typical of developmental studies. Spline models can be useful to developmental researchers for analyzing the time course of event-based changes in eye tracking data.