Wave drag in aerodynamics is drag associated with the shock wave and shock-induced separation. This type of drag appears at transonic and supersonic speeds. The drag from acoustic waves is always negligible. The problem is more general in hydrodynamics, since wave propagation occurs at all speeds for all types of sailing vessels and for most cases of submerged bodies.
There are several ways of dealing with wave drag: use of transonic/supersonic area ruling for wing-body combinations; use of supercritical airfoils, thin wing sections, wing sweep, low-aspect ratio wings, boundary layer control, blunt leading edge (at hypersonic speeds). Less orthodox methods include oblique and anti-symmetric wings (wings never built, in fact).
At transonic speeds some of the main concerns are: driving the drag divergence upward, removing the buffeting and the possible shock stall.
At supersonic and hypersonic speeds a few peculiar problems appear: namely, aerotherodynamic heating, and structural stiffness compatible with volume distribution and wing thickness.
Methods of analysis have long relied on linearized potential theories. At hypersonic speeds Newtonian theories are still common.