Interfaces and discontinuities occur in a variety of computational problems ranging from engineering to computer graphics and a great deal of theoretical and computational effort is usually required to produce numerical algorithms to treat these types of problems. Moreover, these algorithms tend to be complicated and problem specific as one has to enforce the appropriate boundary conditions at the interface or discontinuity. A new numerical technique, the Ghost Fluid Method, has recently been developed to handle interfaces in a robust and efficient fashion leading to a general class of "boundary condition capturing" techniques that can easily be applied to a large number of problems. These techniques are based on identification of "continuous" and "discontinuous" variables at an interface and treating these variables so that one can difference across the interface in a seamless and simple fashion. It is important to note that a special definition of "continuous" is used, e.g. we will define 3 continuous variables across a one-dimensional shock wave.