Experimental and theoretical work on ionizing shock waves in a fully ionized plasma is reviewed for the case in which a magnetic field is imposed parallel to the plane of the shock front. The boundary conditions for ionizing shocks are discussed. It is shown that the additional boundary conditions required for ionizing shock waves follow from the ionizational stability of the gas ahead of the shock front. The front structure of ionizing shocks is analyzed qualitatively: some calculated results are also reported. Experimental results on magnetic structures are discussed. The physical mechanisms which shape the shock front in a plasma are examined. Some results calculated for the front structure in a plasma are reported.