This article reviews the mechanical behavior of a capsule under the influence of viscous deforming forces due to a flowing fluid. It focuses on artificial capsules and vesicles with an internal liquid core enclosed by a very thin membrane with different constitutive laws. The recent modeling strategies are outlined together with their respective advantages and limitations. I then consider the motion and deformation of a single, initially spherical capsule freely suspended in a simple shear or plane hyperbolic flow and discuss the effect of the membrane constitutive law, initial prestress, membrane buckling, and bulk or membrane viscosity. Finally, I consider the flow of spherical capsules in small pores and show how numerical models can be used to evaluate the mechanical properties of the membrane.


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