The rheology of dilute suspensions of core–shell particles has been investigated by several researchers. Three types of core-shell particles are particularly important: solid core-hairy shell particles, solid core-liquid shell particles, and liquid core-liquid shell particles. Hairy microgels fall under the category of solid core-hairy shell particles. An interesting feature of suspensions of microgels and solid core-hairy shell particles, the shell thickness can be increased or decreased by varying the temperature or nature of the dispersion medium. The expression for the zero-shear-rate viscosity of dilute dispersion of solid core-liquid shell particles was derived. Stone and Leal investigated deformation and rheology of dilute dispersions of double-emulsion droplets, that is, liquid core-liquid shell particles. The dipole strength of a single liquid core-liquid shell droplet located in an infinite matrix fluid can be determined using the zero-order flow fields obtained by Stone and Leal.