In this article we discuss the dynamics of a single drop immersed in an immiscible fluid with a given velocity field at infinity. Drop relaxation is also discussed. Newtonian and non-Newtonian fluid components are considered, to examine the effects of constitutive elasticity on drop deformation modes. Both experimental and theoretical results are reviewed. We illustrate in some detail three main issues of research of the last decade, namely, the exploitation of rheo-optical techniques, the study of large deformations and break-up, through numerical simulations, and the advancements in single drop theory for the case of non- Newtonian fluid components.
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