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 solubilization and from 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; such coupling 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, these droplets are fascinating to physicists, chemists, biologists, and fluid dynamicists alike in analyzing viscous self-propulsion and collective dynamics in active-matter systems, developing synthetic cellular models, or performing 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 modeling of these intriguing droplets, together with their experimental design and characterization.