The weighted residual concept of ordinary differential equation solutions is extended to the two problems of continuous linear system identification and model reduction. Although continuous system dynamics are classically described in terms of the system ordinary differential equation, an equivalent integral equation description exists and it is this latter equation which is used as the basis of the various identification and model reduction techniques. Several individual approaches within the broad class of weighted residual approaches are detailed and a number of numerical examples are presented to illustrate the application of such schemes.