Soft particles such as drops, vesicles, and red blood cells, display rich dynamics in externally applied flow and electric fields. For example, vesicles have multiple dynamical states in shear flow (tank-treading, tumbling); drops in uniform electric field undergo various symmetry-breaking instabilities. I will overview the complex flow behavior of these inertialess systems and discuss how it arises from the nonlinear interaction of a deformable microstructure and external forcing.