Many aquatic microorganisms are able to swim and typically do it in a moving, sometimes turbulent, fluid environment. The interaction between swimming (self-propulsion) and flow advection can give rise to interesting phenomenology, especially concerning the spatial distribution of microbes. Many aspects of such interaction can be understood by using ideas and tools from dynamical systems theory and fluid mechanics. Here we shall discuss some of these aspects focusing on the case study of gyrotactic phytoplankton, which swims by means of two flagella opposite to the center of mass, which is displaced with respect to the center of symmetry --- bottom heavy cells.