When sponges were well-behaved, a calcareous skeleton was sufficient for assignment to the Class Calcarea. Since the discovery that some sponges secrete both siliceous spicules and a massive calcareous skeleton (Class Sclerospongia Hartman and Goreau, 1970) and more recently, the discovery of an apparent living Sphinctozoan with an aspicular calcareous skeleton and soft parts like those of a demosponge (Vacelet, 1977b) the picture has become more clouded. The groups to be discussed here originally included all the known sponges with massive calcareous material in the skeleton. They were named Pharetrones by Zittel (1878) who emphasized the skeleton of anastomosing fibers, containing, so he thought, spicules packed side-by-side like arrows in a quiver (pharetra is Greek for “quiver”). Steinmann (1882) noted that in some of the genera included by Zittel as well as in new forms which he described, the skeleton was sheet-like and outlined a series of hollow chambers. Steinmann set apart the chambered types as a subgroup Sphinctozoa(=“constricted animals”) and the fibrous types as the subgroup Inozoa(=“fiber animals”). Steinmann also pointed out that the skeleton of the Sphinctozoa was aspicular and spherulitic. Zittel had illustrated the spherulites but considered them diagenetic. Steinmann, however, observed that the spherulites were bored by endolithic algae or fungi, and were therefore probably original. He also noted that the spicules in some Inozoa were sinuous and unlike typical sponge spicules, and indeed considered the pharetronids not to be sponges at all. Hinde (1884) and others soon demonstrated that the fibers of many pharetronids, as well as the external cortical layer (including that of the sphinctozoan Tremacystia) contained typical triradiates of the Class Calcarea. The discovery of the first living pharetronids (Doederlein, 1892, Kirkpatrick, 1900, 1908) with soft-parts and flesh-spicules typical of the Calcarea, seemed to settle the matter. Rauff (1913) introduced the useful term sclerosome for the non-spicular material of the skeleton, which might range from simple cement between spicules to the entire skeleton. It is this material that recent studies by Wendt (1979, 1980), Cuif and others (1979), and Jones (1979) have shown to be quite heterogeneous and variable. We will now look at the morphology and fossil history of the Inozoa and Sphinctozoa without any commitment as to the biological unity of each group.