The forebrain of actinopterygian fishes differs from that of other vertebrates in that it consists of a pair of solid lobes. Lateral ventricles surrounded by nervous tissue are entirely lacking. Comparative anatomical and embryological studies have shown that the unusual configuration of the forebrain in actinopterygians results from an outward bending or eversion of the dorsal portions of its lateral walls. Due to this eversion, the telencephalic roof plate is transformed into a wide, membranous structure which surrounds the dorsal and lateral parts of the solid lobes and is attached to their lateral or ventrolateral aspects. The taeniae, i.e. the lines of attachment of the widened roof plate, represent important landmarks in actinopterygian forebrains. In the present paper, the process of eversion is specified and quantified. It is pointed out that recent suggestions to modify the original eversion concept lack an empirical basis. Eversion is the antithesis of the inward bending or inversion that occurs in the forebrains of most other vertebrates. The forebrain lobes in actinopterygians, like those in other vertebrates, comprise a pallium and a subpallium, both of which include a number of distinct cell masses. The morphological interpretations of these cell masses over the past 130 years are reviewed and evaluated in light of a set of carefully selected criteria for homologous relationships. Special attention is paid to the interpretation of a cell mass known as Dp, situated in the caudolateral portion of the pallium in teleosts (by far the largest clade of living actinopterygians). Based on its position close to the taenia, and given the everted condition of the pallium in teleosts, this cell mass clearly corresponds with the medial pallium in inverted forebrains; however, Dp receives a dense olfactory input, and it shares this salient feature with the lateral pallium, rather than with the medial pallium of inverted forebrains. There is presently no consensus regarding the homology of Dp. Several recent authors [Wullimann and Mueller, 2004; Yamamoto et al., 2007] consider the lateral pallium in inverted forebrains and Dp in teleosts to be homologous because they believe that these cell masses originate from the same germinative zones, but that Dp attains its ultimate position only through migration. On the other hand, the present author believes that Dp is situated in the immediate vicinity of its germinative zone and that it represents a specialized part of the lateral pallial zone in teleosts, a zone that can be homologized topologically with the medial pallium in inverted forebrains. Further, it is proposed that the lateral olfactory tract in teleosts, which supplies most of the olfactory fibers to Dp, is not homologous to the same-named tract in the inverted forebrains of most other vertebrates.