Systems, components, and methods for attaching insulating foam panels to a wall provide additional insulation by virtue of the low thermal conductivity of the foam material of which the panels are made. Structural elements disposed within the panels provide attachment features used for fixing the panels to the wall, and also provide a structural mounting for finishing materials that may be placed on the wall. A clip attaches to the attachment features and is then affixed to the wall. One or more shims may be attached to the clip for accommodating irregularities in the wall. The shims also may be used in a variety of additional applications where accommodation for irregularities in spacing is desired.