Megafossils from the Ediacaran Period (635-541 Ma) have been controversial in part because many are mere impressions in coarse-grained rocks. New examination of these fossils in petrographic thin-sections reveals various features that inform understanding of the biological affinities of these problematic fossils. Material examined includes Dickinsonia costata from the Ediacara Member of the Rawnsley Quartzite in South Australia, Ernietta plateauensis from the Kliphoek Member of Namibia, Ivesheadia lobata from the Drook Formation of Newfoundland, Charnia antecedens and Charniodiscus spinosus from the Mistaken Point Formation of Newfoundland, Aspidella terranovica from the Fermeuse Formation of Newfoundland, and Nemiana simplex from the Mogilev Formation of Ukraine and the Verkovka Formation of Russia. Three characteristics stand out for all but Nemiana. First, these fossils were remarkably resistant to burial compaction, as originally inferred from depth gauge measurements of overlying moulds, and here confirmed by thin-sections perpendicular to bedding planes. Second, thin-sections reveal a construction of micrometric branching elongate structures forming millimetric hollow elongate structures in fractal arrangements. Third, some of the fossils are asymmetric bifacial or unifacial, with a thick finished upper wall but lower wall thin or non-existent and attached to elongate structures downward into sediment. Compaction-resistant fossils with asymmetric histological layering are most like crustose and fruticose lichens fortified with chitin. In contrast, non-resistant impressions in the tops of beds filled by overlying cross-bedded sediment, as in Nemiana, preserve no informative histology and are similar to lake balls and microbial colonies.