Oblique shock is a shock results from a disturbance from the side of the flow. In the extreme case the disturbance appears in front of the flow and the created shock is referred as normal shock. The oblique shock appears as a shock in angle to flow direction. This shock is common in many situations which include space vehicles (airplane, etc) and many internal flow. The first to discover this shock was Mach in his original picture showing a bullet in a supersonic flow that cause the oblique shock.
The oblique shock analyzed in the same way as the normal shock when flow is "broken" into two components, one in the flow direction and one perpendicular to the flow. The component perpendicular to the flow doesn't go any change and the component in the flow direction undergoes shock. The mathematical treatment for this component is the same as for normal shock. However, because two dimensional nature of the problem, as oppose to normal shock, two parameters have to be provided in order to solve the problem. The first who analytically investigate this physical situation was Ludwig Prandtl with his student T.Meyer 190x. They also discovered the isentropic flow (flow without shock) region. However, they were not able to express the limit of their equations. Due to the mathematical complications, the solution to these equations declared unattainable by NASA in the famous NACA 1135 report. Nevertheless, scientists attempted to solve these equations with various techniques. For example, some mathematicians suggested to solve a more complicated equations with viscosity and find the solution when the viscosity is approaching zero. Other suggested numerical approaches. In last ten years or so partial and limited solution was suggested by Emmual. Recently, Bar-Meir find the complete analytical solution.
Bar-Meir's solution suggests that, contrary to popular believe, oblique shock cannot occur at zero inclination. The other interesting part of Bar-Meir's solution is the explanation for the detach shock. The solution also explains the transition to Prandt-Meyer function.