  In most practical situations, active particles are affected by their
environment, for example, by a chemical concentration gradient, light
intensity, gravity, or confinement. In particular, the effect of an external
flow field is important for particles swimming in a solvent fluid. For
deformable active particles such as self-propelled liquid droplets and active
vesicles, as well as microorganisms such as euglenas and neutrophils, a general
description has been developed by focusing on shape deformation. In this
review, we present our recent studies concerning the dynamics of a single
active deformable particle under an external flow field. First, a set of model
equations of active deformable particles including the effect of a general
external flow is introduced. Then, the dynamics under two specific flow
profiles is discussed: a linear shear flow, as the simplest example, and a
swirl flow. In the latter case, the scattering dynamics of the active
deformable particles by the swirl flow is also considered.
