  The main goal of this paper is to explore the leapfrogging phenomenon in the
inviscid planar flows. We show for 2d Euler equations that under suitable
constraints, four concentrated vortex patches leapfrog for all time. When
observed from a translating frame of reference, the evolution of these vortex
patches can be described as a non-rigid time periodic motion. Our proof hinges
upon two key components. First, we desingularize the symmetric four point
vortex configuration, which leapfrogs in accordance with Love's result
\cite{Love1893}, by concentrated vortex patches. Second, we borrow some tools
from KAM theory to effectively tackle the small divisor problem and deal with
the degeneracy in the time direction. Our approach is robust and flexible and
solves a long-standing problem that has remained unresolved for many decades.
