A look into the microworld reveals plethora of elastic structures in fluidic environments. From biomacromolecules undergoing conformational changes in response to thermal fluctuations, to swimming microorganisms, which display a rich variety of shapes and swimming gaits, and finally to artificial, laboratory-controlled systems capable of propulsion. Despite this diversity, the physics of microscale imposes universal limitations on their motion and propulsion strategies. In my talk, I will review the basic properties of Stokes flows and their consequences for passive and active microscale matter. Next, I will discuss how minimal, coarse-grained models of supercoiled DNA may yield accurate predictions of their shapes and hydrodynamic properties. As an example of active microswimmers, I will present an artificial system of microscale oil droplets with the ability to swim due to a surface phase transition driven by environmental temperature fluctuations. I will demonstrate how a coarse-grained elastohydrodynamic model can be successfully employed to quantitatively describe the motion of droplets.