Understanding how animals control the dynamic stall vortices in their wake is critical to developing micro-aerial vehicles and autonomous underwater vehicles, not to mention wind turbines, delta wings, and rotor craft that undergo similar dynamic stall processes. Applying this knowledge to biomimetic engineering problems requires progress in three areas: (i) understanding the flow physics of natural swimmers and flyers; (ii) developing flow measurement techniques to resolve this physics; and (iii) deriving low-cost models suitable for studying the vast parameter space observed in nature. This body of work, which consists of five research chapters, focuses on the leading-edge vortex (LEV) that forms on profiles undergoing rapid manoeuvres, delta wings, and similar devices. Lagrangian particle tracking is used throughout this thesis to track the mass and circulation transport in the LEV on manoeuvring profiles. The growth and development of the LEV is studied in relation to: flapping and plunging profile kinematics; spanwise flow from profile sweep and spanwise profile bending; and varying the angle-of-attack gradient along the profile span. Finally, scaling relationships derived from the observations above are used to develop a low-cost model for LEV growth, that is validated on a flat-plate delta wing. Together these results contribute to each of the three topics identified above, as a step towards developing robust, agile biomimetic swimmers and flyers.