The authors revise the occurrences of burrow networks with striated walls having dominantly transverse to oblique striae, which have been assigned to the ichnogenera Spongeliomorpha Saporta, 1887, and Steinichnus Bromley & Asgaard, 1979. The taxonomic status of the ichnogenus Steinichnus Bromley & Asgaard, 1979 is examined and it is suggested that this ichnogenus is a subjective junior synonym of Spongeliomorpha Saporta, 1887. Spongeliomorpha is best reserved for an unlined network of burrows having distinct surface ridges or grooves of different orientation and massive filling. The diagnosis of Spongeliomorpha is emended accordingly and the proposed ichnospecies revised for consistency with the diagnostic features of the ichnogenus. Spongeliomorpha milfordensis Metz, 1993a is considered a subjective junior synonym of Spongeliomorpha carlsbergi (Bromley & Asgaard, 1979) after a visual comparison and statistical analysis of the angle of striation with respect to the burrow midline in the type material. Nevertheless, the use of statistical techniques is not advocated for distinction of ichnotaxa, but may support observations. Spongeliomorpha carlsbergi is considered as an indicator of nonmarine settings and was probably produced by burrowing insects. Proposed ichnospecies of Spongeliomorpha that fit the emended diagnosis include S. sudolica (Zaręczny, 1878); S. iberica Saporta, 1887; S. sicula D’Alessandro & Bromley, 1995; S. chevronensis Muñiz & Mayoral, 2001; and Spongeliomorpha isp. nov. aff. sicula Lewy & Goldring, 2006.