We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching two different plane waves Ajeiϕje-2iBjx, j= 1 , 2 as x→ ± ∞. Using Riemann–Hilbert techniques and Deift–Zhou steepest descent arguments, we study the long-time asymptotics of the solution. We detect that each of the cases B1< B2, B1> B2, and B1= B2 deserves a separate analysis. Focusing mainly on the first case, the so-called shock case, we show that there is a wide range of possible asymptotic scenarios. We also propose a method for rigorously establishing the existence of certain higher-genus asymptotic sectors.