The concept of adjoint system (sometimes, also called conjugate system, transposed system, etc.) has been defined and used in different ways in different fields of science and engineering for different purposes, and the theories and techniques in different fields have been developed more or less independently. In the present paper it will be illustrated that the concept can be somehow related to the numerical-computational technique of fast automatic differentiation in any field, and that its efficiency in theory and application can be better understood from the numerical-computational viewpoint.