  Microscopic active droplets are able to swim autonomously in viscous flows:
this puzzling feature stems from solute exchanges with the surrounding fluid
via surface reactions or their spontaneous solubilisation, and the interfacial
flows resulting from these solutes' gradients. Contrary to asymmetric active
colloids, these isotropic droplets swim spontaneously by exploiting the
nonlinear coupling of solute transport with self-generated Marangoni flows,
which is also responsible for secondary transitions to more complex individual
and collective dynamics. Thanks to their simple design and their sensitivity to
physico-chemical signals, they are fascinating physicists, chemists, biologists
and fluid dynamicists alike to analyse viscous self-propulsion and collective
dynamics in active matter systems, to develop synthetic cellular models or to
perform targeted biomedical or engineering applications. I review here the most
recent and significant developments of this rapidly-growing field, focusing on
the mathematical and physical modelling of these intringuing droplets, together
with its experimental design and characterisation.
