The hyperbolic conservation laws that govern the fluid dynamics flows and the magnetohydrodynamics flows exhibit exciting nonlinear flow features such as shock waves and expansion fans for various flow regimes of interest in the high-speed flows. The interaction of the shock waves with the flow field and with itself gives rise to a myriad of fascinating flow features. The study of the shock interactions in the gas-dynamic flows was of particular interest for the efficient design of various supersonic and hypersonic flow vehicles, missiles, and rockets. The need for the efficient design of the supersonic vehicles led to the investigation of the shock interaction phenomenon in the steady, pseudo steady and unsteady flows involving wedges and other solid bodies. When compared to the flows over various bodies, the shock interactions present in the open jets received less attraction in terms of studying the reflection phenomenon and their transition criterion. In the present study, the shock interactions happening in the open jets is studied numerically and analytically, and an estimation of the Mach stem height is developed using the modern methods developed for wedge flows. The second part deals with the unsteady shock diffraction over a cylindrical body in the magnetohydrodynamics (MHD) flow field. The MHD flows differ from the ordinary fluid dynamics/gas dynamical flows by the complex interaction of the magnetic field with the flow properties. The flow field changes significantly and accommodates various types of shock waves due to the presence of a magnetic field. In this present study, the unsteady shock diffraction over a cylindrical body will be studied, and the changes in the shock structure and flow field will be discussed when compared to the hydrodynamic flows.