The proliferation of "species" -- often placed in the "wrong" genus, has impacted all taxonamic work in 20th Century hepaticology. The same species may have been described under 3-4, or more, genera; under a single genus, such as Lepidolejeunea, species have been described in some 10-12 genera. The greatest outstanding need is for a synthesis that attempts to critically define families and, in particular, genera and subgenera. For more than a century nobody has attempted such a synthesis. This work attempts to answer this need by providing a modern synthesis of what we have learned, mostly in the second half of the twentieth century, about the families and genera of liverworts. It deals primarily with the conceptual bases that underlie a modern classification of the Hepaticae: the boundaries of suborders, families and genera are drawn by evaluating modern criteria. In such an evaluation emphasis is on features largely unused prior to 1950: ramification patterns and branch origins; capsule wall anatomy; seta and stem anatomy; oil-bodies and cell wall criteria. 211 figures, drawn by the author, illustrate these features and also show many taxa in drawings illustrating basic aspects of each genus. Almost all larger groups were studied from living plants and emphasis is on liverworts as living organisms. The larger genera of Hepaticae are each illustrated with several plates and emphasis is on "key" genera which occupy critical phylogenetic positions, such as Lepidozia, Pseudocephalozia and Paracromastigum. No attempt is made at species diagnoses but generic boundaries, in larger genera, are defined by illustrating several species per genus. Except for genera with numerous species, keys to species are provided. In numbered annotations diverse problems, such as generic relationships and boundaries, are discussed; key species are often treated at length. As noted in the Introduction, since all taxa cannot be illustrated and/or described, for all larger genera the "type" method is used: boundaries are established by treating (and illustrating) key taxa so as to draw logical boundaries for each genus -- and family. The author has conducted field work in the Antipodes for over 40 years, starting in Fuegia in 1960. He has not only become familiar with all the chief groups as living plants, but has studied them microscopically in areas as diverse as Fiji, the Prince Edward Islands., Campbell I., Chile and New Zealand, residing for months or sometimes years in these regions. The opportunity to study hepatics in the field has given him a unique opportunity to learn these organisms as living entities; to drawt cytological details from living plants, and to place critical material into FAA for subsequent illustration, especially of the ephemeral sporophytes. Unlike most extant taxonamic works, which are based on herbarium study, this work tries to give the reader a "feeling" for the many taxa as living organisms.