The controllability and stability of shock waves are of fundamental importance in a wide range of scientific and engineering applications, including aerodynamics, aerospace engineering, explosion mitigation, and shock tube experiments. In this talk, we present several controllability problems and related stability issues arising in the control of multidimensional steady shock waves. In particular, we discuss recent progress in the analysis of these problems, focusing on the control of both the leading shock waves generated by wedges or conical bodies and the associated fluid flows. One of the objectives is to design wedge or cone boundary geometries that achieve prescribed pressure distributions and/or specified shock locations. We will also outline future perspectives and highlight several open problems in this direction.