The microscopicworld is surprisingly busywith swimming micro-organisms. In a droplet of pondwater, there can be tens of thousands of microbes. They are predators and preys, producers and consumers, and they formthe bottom levels of the ecology of our world. The swimming micro-organisms can be in general classified into prokaryotes and eukaryotes. Eukaryotes come later in evolution. They are higher organisms than the prokaryotes as they possess more complex cellular structures such as the nucleus and mitochondria. Motile eukaryotic micro-organisms all use an active hair-like structure for swimming, known as flagella or cilia. Although nuanced difference exists between flagella (cilia) of different species, their general internal structure and driving mechanisms are mostly the same. In some sense, they are one of the bestselling machines for locomotion on themicron scale. Although flagella are the first-ever documented organelles in cell biology, our understanding of them is still limited. For example, we have only begun to appreciate how the conformational change of single protein motors results in the waveformon the scale of a flagellum. Our understanding of the flow generated by even a single flagellum is rudimentary: resolving the temporal features of such flow field remains experimentally challenging. On a larger scale, how thousands of cilia interact with each other to facilitate fluid transport is still elusive: theoretical models and simulations are waiting for experimental verification. In this thesis, I explore different topics centering around flagellar/ciliary motility by employing novel experimental and numerical techniques, and hence advance our understanding. My experimental investigation starts by resolving the flow generated by the beating cilia of single cells. Due to the high beating frequency, high temporal resolution is required to map the time-varying flow field, which conventional tracer particle-based flow velocimetry techniques cannot provide. To tackle this challenge, I implemented an optical tweezers-based flow velocimetry (OTV) technique. In this technique, a bead is trapped and placed at a particular location by a focused laser beam. The local flow displaces the bead from the trapping center. This displacement, although small, can be accurately monitored by laser interferometry and converted into an electrical signal by photoelectric detectors. Essentially,we gain the desired accuracy and temporal resolution by exploiting the high resolution and large bandwidth of interferometric and electrical measurements. With this technique, I revealed that the ciliary flow deviates fundamentally fromhow it is often modeled by Stokes equations. More specifically, the flow’s amplitude decays faster spatially, and its phase shifts over distance. These discrepancies are resolved by adding a linear unsteady term to Stokes equations. Furthermore, I systematically characterized the ciliary flow field created by captured C. reinhardtii cells. The flow field in different directions and over the ciliary beating plane are measured experimentally, modelled numerically, and analyzed theoretically. Results displayed excellent agreement with each other, and altogether increased our knowledge in the ciliary flow. With the OTV measurements, I not only studied the basic hydrodynamics of ciliary flowbut also addressed a long-standing hypothesis regarding the function of a ciliary appendage. Many cilia have fibrous ultrastructures called mastigoneme. These fibrous appendages are believed to help cells swim faster by increasing the ciliary surface area. Our experiments, together with numerical studies, completely refute this hypothesis: such fibrous hairs do not show any hydrodynamic significance in C. reinhardtii. Instead, its absence in genetically modifiedmutants appeared to result in some behavioral changes, causing the cells to turn abruptly more often than usual. Therefore, I have re-opened the question about the function of the fibrous mastigonemes. Future investigation towards this direction is needed and is likely to lead to more exciting findings. Lastly, I attempted to bridge the physics of ciliary flowwith the biology of ciliary beating. I focused on the ciliary difference and investigated it by selectively loading each cilium of C. reinhardtii with external flows. The ciliary difference is critical for the steering of biflagellates (micro-organisms swimming with two flagella/cilia). I observed an unreported functional difference between the two cilia, as I found that the coupling between the two cilia is unilateral. One cilium serves as the coordinator of beating, and a cell is coupled to external hydrodynamic forces mostly through this coordinating cilium. Altogether, by introducing the OTV technique and incorporating different numerical methods, I was able to elucidate the ciliary flowin a time-resolvedway, updating the current understanding in these unsteady flows. The effectiveness of this methodology was demonstrated again by its application in studying the function of the fibrous ultrastructures. By further moving on to the biological aspect of ciliary beating, we found a new type of difference between the two cilia, which enriches our knowledge in inter-ciliary coupling.