Mollusca is the second most speciose phylum of animals and includes a high organizational diversity grouped in eight classes, with the gastropods and bivalves being most familiar. The phylogenetic relationships among the three aculiferan molluscan classes Solenogastres (Neomeniomorpha), Caudofoveata (Chaetodermomorpha) and Polyplacophora (Placophora, chitons, Loricata), as well as the sister-group relationship to Conchifera (all other molluscs) are still under discussion. On one side, the three aculiferan groups are regarded as a monophyletic clade, Aculifera, contrasted with its sister taxon Conchifera (Aculifera concept). Recent molecular-phylogenomic analyses appear to support this hypothesis. Here we point out the plesiomorphic nature of many morphological similarities among the aculiferan taxa and in relation to Conchifera. On the other side, a complex of morphological synapomorphies support Recent Polyplacophora as sister group to Conchifera (Testaria concept). The supposed monophyletic characters for this clade Testaria (Recent Polyplacophora + Conchifera) include the radula complex, the specific differentiation of the midgut into regions, the dorsoventral musculature, and the excretory organs. A critical review of arguments of both hypotheses in the light of present evidence, also integrating ontogenetic and palaeontological data, is presented. Morphological analyses favour the Testaria concept, implying a gradual anagenesis from aplacophoran to polyplacophoran grades and a monophyletic Testaria. Recently published molecular trees differ conspicuously in the position of Aculifera as well as in conchiferan relationships and show well-supported but conflicting aculiferan and conchiferan topologies. These discrepancies are discussed in connection with outgroup representation, the rooting of Mollusca, and refining of phylogenomic analysis tools. Although considerably improved, current molecular analyses of 'deeper' relationships within major molluscan taxa appear less reliable than the morphological Testaria concept.