Characteristic treatments of boundary conditions for Euler and Navier Stokes equations rely on computing the strength of the waves entering the computational domain as a function of the strength of the outgoing waves and of the physical boundary conditions imposed on the boundary. Even though this rule is common to all characteristic conditions, the technique used to evaluate the strength of the waves (temporal or spatial derivatives) is not unique and leads to very different results. A general framework for these boundary conditions is described, in which all methods can be written either in terms of temporal derivatives ({\em temporal form}) or in terms of spatial derivatives ({\em spatial form}). This allows a direct formal comparison of boundary treatments which have been originaly proposed in completely different forms. Some existing formulations for inviscid compressible flow are compared, in terms of theory and of results in certain test cases. This comparison provides a systematic explanation to the side-effects observed when using one of the existing formulations for boundary conditions.