The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years:​ Part I explains the behaviour of individual microorganisms, and Part II explains collective behaviour. Since the discovery of microorganisms by van Leeuwenhoek in the 17th century, many natural scientists have been interested in their motility because it is directly associated with biological function. A research upsurge occurred in the 1970s, with the elucidation of swimming mechanisms among individual microorganisms and the theoretical derivation of swimming speeds. Various swimming strategies of three types of microorganisms, i.e. bacteria, ciliates and microalgae, are explained in this Part I. We show that some of the behaviours of microorganisms can be described by biomechanical equations and are to some extent predictable. Recent researches have revealed the behaviour of microorganisms in more complex environments and more realistic settings, which are also reviewed in the paper. Last, we provide future prospects for research on microbial behaviour.