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This paper discusses some general aspects and techniques associated with thelong-time asymptotics of steplike solutions of the Korteweg--de Vries (KdV)equation via vector Riemann--Hilbert problems. We also elaborate on anill-posedness of the matrix Riemann--Hilbert problem for the KdV case in theclass of matrices with square integrable singularities. Furthermore, we refinethe asymptotics for the shock wave in the Whitham zone derived previously andrigorously justify it for a more general class of initial data. In particular,we clarify the influence of resonances and of the discrete spectrum on theleading asymptotics.

Asymptotics of KdV shock waves via the Riemann-Hilbert approach