In this paper, models of the blood glucose (BG) dynamics in people with Type 1 diabetes (T1D) in response to moderate intensity aerobic activity are derived from physiology-based first principles and system identification experiments. We show that by enhancing insulin-dependent glucose utilization by the tissues in two phases, a rapid short-term increase in insulin-independent glucose clearance and augmented glucose uptake, and a long-term sustained increase sensitivity to insulin action, a metabolic model able to reproduce the effects of activity on glucose disposal is obtained. Second, a control-oriented transfer function model is proposed to predict the BG response to an exercise bout modeled as a step change in heart rate (HR). Results comparing model predictions with actual patients data collected in a series of experimental sessions including physical activity (PA) are presented. The findings will contribute to the design of a fully automated closed-loop for improved glucose control in conditions of daily life for people with T1D.