in an exciting paper, j. bedrossian and n. masmoudi established the stability of the 2d couette flow in gevrey spaces of index greater than 1/2. i will talk about recent joint work with n. masmoudi, which proves, in the opposite direction, the instability of the couette flow in gevrey spaces of index smaller than 1/2. this confirms, to a large extent, that the transient growth predicted heuristically in earlier works does exist and has the expected strength. the proof is based on the framework of the stability result, with a few crucial new observations. i will also discuss related works regarding landau damping, and possible extensions to infinite time.