In this thesis, the dynamic behavior of droplets including the coalescence of a falling droplet with a sessile droplet on solid, and shedding of a sessile droplet exposed to shearing airflow are studied numerically. A two-phase volume of fluid (VOF) method is used to determine the droplet flow, shape evaluation, and contact line movement. The flows studied are treated as being laminar and computed in the framework of the finite-volume numerical method. To validate the model, the results of simulations for maximum spreading diameter of coalescing droplets are compared with experiment. The effect of different parameters such as droplet diameter, the impact velocity, the distance between the impacting droplets, and surface wettability on maximum spreading length, contact time and restitution coefficient are studied and compared to the experimental results.  It has been found that the contact time is independent of the impact velocity in a wide range of velocities; however, it largely depends on droplet diameter. The evolution of surface shape during the coalescence of two droplets on various surfaces is computed numerically and compared with experimental results. The spread length of two coalesced droplets along their original center is also predicted by the model and compared well with the experimental results. Finally, the fundamental parameters determining the incipient motion for a droplet exposed to shearing airflow (runback) are investigated. It was found that wetting parameters such as contact angle and contact angle hysteresis are very influential in determining the minimum required air velocity for drop shedding.