Refractory modules and other insulating modules, which include a plurality of insulating module layers arranged with their major surfaces in a side-by-side orientation, are provided. Each insulating module layer includes a first section having a slot extending into a joint edge and a second section having a tab extending from a joint edge. The first and second sections each comprise a refractory insulation material, which typically includes a fibrous refractory material. The tab has an outer contour and the slot has an inner contour which substantially corresponds in shape such that when the tab is inserted in interlocking engagement into the slot, the joint edges of the first and second sections are held in juxtaposition along a section juncture.