The liquid flow inside, and the induced air flow around, a falling droplet in stagnant air was numerically investigated using the volume of fluid method to describe the droplet interface. The droplet consisted of oil with the same surface tension and with viscosity as parameter. It was injected into stagnant air with an initial velocity of 1 m/s; therefore, the initial Weber (We = 0.14), Reynolds (Re = 141), and Bond (Bo = 2.4) numbers remained constant during the parametric study whilst the initial Capillary (Ca) and Ohnesorge (Oh) numbers varied by an order of magnitude from 0.46 to 4.6 and from 0.044 to 0.44, respectively. We examined the effect of viscosity on the flow inside, and around, the droplet as well as on the droplet deformation and its natural frequency. This investigation showed a strong dependence of the deformation with liquid viscosity. Specifically, the droplets achieved their final deformation in under-damped, for low viscosity, and in over-damped, for high viscosity, oscillation modes. After a critical time tcrit (or Recrit), the instantaneous air flow symmetry was disturbed, initially in the wake and soon after in the interior of the droplet and in the vortex shedding downstream of the droplet. The air flow in the wake region detached from the droplet surface and resulted in a wake which was approximately 1.5 times longer and wider than the wake behind a solid sphere at the same Re number at steady state conditions. A roller-vortex structure (called rollex) was established upon injection in the immediate wake of the droplet, forming the necessary kinematic link between the directions of the internal circulation in the droplet (Hill vortex) and of the external recirculating air flow in the droplet’s wake. The droplet drag coefficients were compared with corresponding values used in droplet breakup models: although, ultimately, the droplet drag coefficient converged to the values given by the models, the initial magnitudes after injection were incorrect.