Small-scale flow dynamics are important to plankton in delivery of nutrients, sensory detection by and physical encounter with predators, accumulation of bacterial populations in the 'phycosphere' or region immediately surrounding phytoplankton cells and coagulation of cells themselves as a mechanism terminating blooms. In nature, most organisms in upper mixed layers and bottom boundary layers experience unsteady flows. Velocities near the individual vary with time due to the intermittency of turbulence, to discontinuous, spatially distributed pumping by suspension feeders or to the organism's own unsteady swimming behavior, yet most laboratory mathematical and laboratory models at low Reynolds numbers (Re) have used steady flows. Moreover, despite the fact that accurate derivations for simple geometries date back to Boussinesq in 1885, models of unsteady flows at low Re have largely been ignored in biological applications. Objects at very low Re perturb the flow large distances away (of order 100 object radii). A consequence for an object in the range of 0.1 to 1 mm in diameter, shortly after an acceleration begins, is that accelerations are substantially resisted by a so-called 'history' term that accounts for the need to change this spatially extensive flow field or 'wake.' For this size range (a common one for plankton, including many larvae and most species of phytoplankton) and the normal density (specific gravity) range of organisms, the effect is generally larger in magnitude and longer lasting than the more familiar 'acceleration-reaction' or 'added-mass' term. New singularity solutions from mechanical engineering make calculations for realistic organism shapes feasible, and PIV methods allow experiments in unsteady flows.