A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. In this talk I will introduce new gluing methods for 3d Euler flows which provide a mathematical justification of leapfrogging phenomenon by constructing a smooth solution of the 3d Euler equations exhibiting this motion pattern. (Joint work with Juan Davila, Manuel del Pino and Monica Musso.)