Fluid mechanics plays a crucial role in many cellular processes. One example is the external fluid mechanics of motile cells such as bacteria, spermatozoa, and essentially half of the microorganisms on earth. These organisms typically possess flagella, slender whiplike appendages which are actuated in a periodic fashion in a fluid environment, thereby giving rise to propulsion. The type of periodic actuation which cannot be exploited for locomotion was established in 1977 by Purcell, and is referred to as the Scallop theorem: It states that, due to the linearity of Stokes's equations of motion, time-reversible movement (i.e. movement that is identical under time-reversal) cannot not lead to any average locomotion. In this talk, we ask the following question: What ingredients are necessary to escape the constraints of the Scallop theorem? We will discuss in particular the role of body kinematics, flow and swimmer inertia, collective motion, and the physical nature of the surrounding fluid.