A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. It was discovered in the 1980s via numerical methods that small-amplitude Stokes waves are unstable with respect to transverse perturbations of the initial data. We will discuss our recent rigorous proof of these transverse instabilities in both the infinite and finite depth cases. Joint work with W. Strauss and R. Creedon.