Swimming in a very viscous fluid like corn syrup? That must be something we never want to do. But this tough exercise is in fact just a normal living for the vast majority of the organisms inhabiting the earth. For microorganisms such as bacteria or algae, fluid mechanics is totally different from what we know from our daily experiences. Since they are so small, few tenth of micron-meter at most, they have to survive in the world of very low Reynolds number, where viscous dissipation dominates over fluid inertia. In this talk, we will first look at how different such a world is from our intuition, along with several important physics on the low Reynolds number hydrodynamics. Since at this length scale, the most common form of cellular systems are the elastic filament, life is a consequence of coupling between dissipation and elasticity. As an example, I will talk about how Spiroplasma bacteria swim. Spiroplasma is a tiny, helical-shaped filamentous eubacterium. Its motility is distinct from those of many other familiar examples such as E. Coli. I will show, comparing to recent video-microscopy observations, some recent theoretical results on the Spiroplasma motility obtained from the hydrodynamic study based on an elastic filament model. Its implications for a developmental consequence in this microbiological system may also be illustrated.