Dispersive partial differential equation are usually set on an unbounded domain. When building a numerical scheme, it is therefore mandatory to extract a bounded computational domain and to set boundary conditions. The derivation of adapted boundary conditions is therefore of matter importance to obtain a solution that may be the restriction of the solution existing on the initial unbounded domain. We will review in this talk the various ways to obtain what is known as transparent boundary conditions and we will explain to approximate them to obtain convergent numerical schemes.