The present study investigates the mechanisms of wake-induced flow dynamics in tandem National Advisory Committee for Aeronautics 0015 flapping foils at low Reynolds number of Re = 1100. A moving mesh arbitrary Lagrangian–Eulerian framework is utilized to realize the prescribed flapping motion of the foils while solving the flow via incompressible Navier–Stokes equations. The effect of the gap between the two foils on the thrust generation is studied for gaps of 1–10 times the chord of the downstream foil. The mean thrust as well as the propulsive efficiency vary periodically with the gap indicating alternate regions of higher and lower thrust generation, emphasizing the profound effect of upstream foil's wake interaction with the downstream foil. Five crucial wake–foil interactions leading to either favorable or unfavorable conditions for thrust generation are identified and different modes depending on the interactions are proposed for the tandem flapping foils. It is observed that the effect of the wake of the upstream foil on the downstream foil decreases with increasing gap. The study also focuses on the effect of the chord sizes of the upstream and the downstream foils on the propulsive forces, where the chord of the upstream foil is selected as 0.25–1 times the downstream foil's chord length. The effect of the chord size on the thrust is noticed to diminish as the chord size of the upstream foil decreases. Furthermore, the effect of the phase difference between the kinematics of the upstream and the downstream foils on flow dynamics is also explored along with its relationship with the chord sizes. For a fixed chord size, the effect of the phase difference on the propulsive performance is observed to be similar to that by varying the gap between the foils due to similar type of vortex interactions. The mechanisms of vortex interactions are linked to provide a comprehensive and generic understanding of the flow dynamics of tandem foils.