Various theoretical and computational aspects of the fluid dynamics of sprays are reviewed. Emphasis is given to rapidy vaporizing sprays on account of the richness of the scientific phenomena and the several, often disparate, time scales. Attention is given to the behavior of individual droplets including the effects of forced convection due to relative droplet-gas motion, Stefan convection due to the vaporization or condensation of the liquid, internal circulation of the liquid, interactions with neighboring droplets, and interactions with vortical eddies. Flow field details in the gas boundary layer and wake and in the liquid droplet interior are examined. Also, the determinations of droplet lift and drag coefficients and Nusselt and Sherwood numbers and their relationships with Reynolds number, transfer number, Prandtl and Schmidt numbers, and spacing between neighboring droplets are extensively discussed. The spray equations are examined from several aspects; in particular, two-continua, multi-continua, discrete-particle, and probabilistic formulations are given. The choice of Eulerian or Lagrangian representation of the liquid-phase equations within these formulations is discussed including important computational issues and the relationship between the Lagrangian method and the method of characteristcis. Topics for future research are suggested.