Plankton provides the most important route of injection of solar energy into the biosystem. It is therefore of major importance to attain a deep understanding of swimming motility and swarming of these microorganisms. As their natural habitats include turbulent (oceanic photosphere) and still (lacustrine) waters as well as the benthic (seafloor) areas, a wide variety of geometries and flow conditions are to be studied. We discuss a number of phenomena found recently in both natural single-cell swimmers (Chlamydomonas reinhartii) and artificial liquid microswimmers consisting of self-propelling 'oil' droplets. Some emphasis is given to properties which may be relevant for biofilm formation, such as adhesion and swarm formation, in particular in non-trivial geometries.