Motivated by the propulsion of spermatozoa, the seventh chapter focuses on the planar waving of eukaryotic flagella. We first show how to apply resistive-force theory to compute the swimming speeds of simple flagellar waves and detail how wave geometry influences locomotion. Next we introduce a measure of swimming efficiency and show how to use it in order to derive the shape of the optimal waving motion. Finally we model the eukaryotic flagellum as an active filament where actuation from molecular motors is accounted for in a continuum manner and the waving motion is obtained as a mechanical balance between molecular forcing, fluid dynamics and passive elasticity. We close with a demonstration of how that model allows us to quantify cellular energy consumption.