The long time asymptotics of the steplike solutions of the KdV equation on the constant backgrounds has long been well studied at the physical level of rigor. This talk will present some recent mathematically rigorous results that refine and justify the above-mentioned asymptotics. We will also compare the efficiency of the two most common methods --- the Nonlinear Steepest Descent and the Inverse Scattering Transform -- for obtaining the soliton asymptotics over a larger space-time domain and for the most general possible class of steplike initial data.