In this review, the general background is provided on cyanobacteria, including morphology, cell membrane structure, and their photosynthesis pathway. The presence of cyanobacteria in nature, and their industrial applications are discussed, and their production of secondary metabolites are explained. Biofilm formation, as a common feature of microorganisms, is detailed and the role of cell diffusion in bacterial colonization is described. Then, the discussion is narrowed down to cyanobacterium Synechocystis, as a lab model microorganism. In this relation, the morphology of Synechocystis is discussed and its different elements are detailed. Type IV pili, the complex multi-protein apparatus for motility and cell-cell adhesion in Synechocystis is described and the underlying function of its different elements is detailed. The phototaxis behavior of the cells, in response to homogenous or directional illumination, is reported and its relation to the run and tumble statistics of the cells is emphasized. In Synechocystis suspensions, there may exist a reciprocal interaction between the cell and the carrying fluid. The effects of shear flow on the growth, doubling per day, biomass production, pigments, and lipid production of Synechocystis are reported. Reciprocally, the effects of Synechocystis presence and its motility on the rheological properties of cell suspensions are addressed. This review only takes up the general grounds of cyanobacteria and does not get into the detailed biological aspects per se. Thus, it is substantially more comprehensive in that sense than other reviews that have been published in the last two decades. It is also written not only for the researchers in the field, but for those in physics and engineering, who may find it interesting, useful, and related to their own research.