Abstract: Exterior insulating building wall panels are disclosed. The wall panels comprise an insulating plastic foam board having disposed therein one or more structural reinforcing members strong enough that the wall panel can be used to span between primary structural framing members of the building without surface supporting assistance from any intervening structural element or supporting substrate. In the preferred embodiments, Truss T's are embedded in channels in the plastic foam board, parallel to each other, and are held in the channels by beds of adhesive and perimeter C-channels. The wall panels are mounted to the building primary framing members by clips which are e.g. welded to the primary framing member and are movably mounted to the structural reinforcing members in the wall panel. Methods of fabricating the wall panels, and methods of installing the wall panels on buildings are also disclosed, as well as the resulting building structural wall system.