I will present a story of how a chance observing run kicked off more than a decade of exploration of the dynamics of the Magellanic Clouds, leading to the discovery, from line-of-sight velocities and Ca triplet abundances, that ~5% of the stars in the inner LMC actually appear to belong to the SMC. The existence of this debris agrees well with a scenario in which the Clouds collided directly with each other, and provides a natural explanation for the star formation activity in 30 Doradus and the LMC microlensing signal, and may be linked with star clusters with multiple populations.  I will show how Gaia DR2 resolves the ambiguity present in our line-of-sight velocity data and allows us to consider the geometry of the debris.  These results were motivation for the SMASH survey, with which we are mapping the debris from the LMC/SMC interaction, exploring their star formation histories, and have discovered new structures around the Clouds and potential companion dwarf galaxies.