The first step on the way to understanding the complicated dynamics of spray is to study the behavior of isolated droplets. In many industrial and natural processes such as turbulent combustion, agricultural sprays, spray cooler, falling raindrops and cloud evolution the droplet is subjected to a chaotic unsteady external flow field. The interaction between the liquid and gaseous phases results in very intricate droplet dynamics like capillary instabilities, atomization, droplet collision and coalescence and vaporization, to name a few. In this dissertation, the focus is on shape oscillations, atomization and vaporization dynamics of pendant and sessile droplets. A droplet residing on a substrate which vibrates vertically at ultrasonic frequency will exhibit different modes of shape oscillation. The competition between capillary forces and inertia forces is basically responsible for these oscillations. However, when an acoustic force field is introduced asymmetrically around the droplet, we discover with the help of ultra high-speed imaging, a new droplet spreading phase. This new method of droplet manipulation could nd application in micro fluidics and lab-on-a-chip systems. By lading the droplet with nanoparticles, the spreading rate can be easily controlled. The spreading phase is followed by an atomization phase where surface ligaments grow to disintegrate into daughter droplets; the intensity of atomization is found to decrease with increase in fluid viscosity. The ability to control atomization characteristics of droplets by lading them with nanoparticles is a powerful technique that may be implemented in spray coolers and combustors to control the spray characteristics or combustion efficiency. Both the spreading and ligament dynamics have been theoretically simulated and the physics behind the observed trends is explained. The growth rate of the ligaments is found to be governed by Weber number modified to include the acoustic pressure level of the standing wave. The frequency of ligament breakup is found to decrease with fluid viscosity and this observation is adequately supported by a theory developed based on the evolution crater on the droplet surface. Turning now to the pendant droplets, by decomposing the droplet shape into Legendre modes, the shape oscillations exhibited by a droplet hanging from the junction of cross-wire placed at the center of an air jet is studied. Both high-speed imaging and hot-wire anemometry are employed. The driving force of oscillation of droplets subjected to the air jet is proved to be the inherent pressure fluctuations in the jet. The effect of surface tension, viscosity and Reynolds number on the shape oscillation level has been examined. The first experimental evidence of viscous attenuation of lower frequencies in a particular mode in glycerol/water mixture is reported. A theoretical model was developed to simulate the droplet shape oscillations induced by different ambient flow fields like pulsatile flow, vortical flow and flow with broadband energy spectrum. The time of interaction of the droplet with an eddy in the flow is found to be very crucial in determining the amplitude of oscillation of the droplet. The shorter the interaction time, the higher are the chances of the droplet oscillation being pushed into resonance. Finally, the heat transfer and droplet regression dynamics of pendant droplets in a hot air stream of various chemical compositions (like conventional fuels, alternative fuels and nanosuspensions) have been experimentally analyzed using high speed imaging. The droplet is deployed at the junction of cross-wire at the centre of a vertical air jet. A hybrid timescale has been proposed which incorporates the effects of latent heat of vaporization, saturation vapor pressure and thermal diffusivity. This timescale in essence encapsulates the different parameters that influence the droplet vaporization rate. The analysis further permitted the evaluation of the effect of various parameters such as surrounding temperature, Reynolds number, far-field vapor presence, impurity content and agglomeration dynamics (nanosuspensions) in the droplet.