This paper makes a comprehensive examination of likely sources that may give rise to higher-order iterative learning control (ILC) laws. Possibilities considered are higher-order model structure, improved learning speed, minimization of various quadratic cost functions, ILC designs based on predictive control, pole placement, direct and indirect adaptive control, and noise filtering. It is shown that among these possibilities, only a non-standard case of pole placement and noise filtering will naturally result in iterative learning controllers with orders higher than one.