This chapter provides a tutorial on the analytical modeling of the nonequilibrium dynamics of particles enclosed by viscoelastic membranes, such as vesicles and capsules. A particular challenge for this kind of problem stems from asphericity and membrane inextensibility, which engenders nonlinearity that gives rise to unexpected behavior, such as multiple dynamical states of vesicles in shear flow (tank-treading, tumbling, trembling, swinging), asymmetric slipper-like shapes in Poiseuille flow, and pearling and asymmetric dumbbell shapes in straining flows or uniform electric fields. We derive solutions for the deformation and motion of a nearly spherical particle, which illustrates the use of a formalism based on spherical harmonics. In particular, we show how a theoretical analysis of the motion and deformation of a freely suspended capsule (referring to both vesicles and polymer capsules) subject to forces arising from applied flows, electric fields, or actively generated surface tractions explains some of the experimentally observed responses. The results are applied to the analysis of blood flow in the microcirculation, and microorganism swimming.