Cilia/flagella are whip-like, cellular appendages, widely conserved across the eukaryotes, that move a single cell through fluid, or move fluid across epithelial tissue. The flagella in the biflagellate alga Chlamydomonas reinhardtii are homologous to those found in humans, for example in sperm cells, and therefore, studying flagella in the algae can shed light on human disease. In this thesis, I develop a new quantitative framework for characterising flagellar activity, beginning by tracking the waveforms of C. reinhardtii flagella, and using the tracked waveforms to estimate various parameters that are relevant to flagellar beating, including frequency, amplitude, synchrony, hydrodynamic and elastic moments, curvature propagation and beat variability. These parameters have been estimated for wild-type and outer-dynein mutant flagella, as well as those immersed in a higher-viscosity medium, and for actively regrowing flagella. The results show that flagella of the mutant strain propagate weaker beats than in the wild type, while those in a raised viscosity are weaker still. For example, in a novel measure of the strength of curvature propagation, the mutant is 38% weaker, and the high-viscosity flagella 80% weaker, than the wild type. Additionally, the dynein mutant shows increased variability of the centre of force, but not the beat frequency. These results could aid with diagnosis of diseases caused by defective cilia, such as primary ciliary dyskinesia, as well as gaining further insight into the mechanisms of diseases caused by excessively viscous mucus, such as cystic fibrosis. Regrowing flagella were found to gradually recover their full-length parameters, but this increase in length was accompanied by an increase in the noise with which they beat, and a temporary aberration in the other flagellum.