The steady propagation of the one-dimensional detonation wave in heptane/air sprays was computationally studied using detailed chemistry, with emphasis on the effects of droplet heating, vaporization, and drag, as well as momentum and heat loss on the detonation velocity and quenching. Results show strong coupling between these processes and the detonation response, leading to a variety of interesting phenomena such as drag-induced concentration of droplets; interference of thermal runaway by cooling due to droplet vaporization; one-stage vs two-stage ignition; chemical heat release controlled by either Arrhenius kinetics or droplet vaporization; internal vs external loss in causing quenching; nonlinear feedback between integrated loss, chemical heat release, and detonation velocity that is responsible for quenching; and the strong influence of the postshock specific heat of the fuel vapor. Consequently, we show that there exist optimum droplet sizes for higher detonation velocities and wider quenching limits and that, depending on the droplet size, higher droplet loading of the spray can also promote detonation propagation and extend its quenching limits.