Germaine Greer set herself to follow up every historical reference to women who painted, whether or not examples of their work could be found; and this for the most part represents the results of that prodigious labor. ""The First Dutch flower paintress was probably Margaretha van Godewijk, who also embroidered flowers and landscapes. Women outside Italy were also successful as portraitists in the sixteenth and seventeenth centuries."" For many, it may be enough to know that they indeed existed; and Greer also discusses the problems of tracing their oeuvre -- their best unsigned paintings having been attributed, she realistically presumes, to the men with whom they (so frequently) worked. But preceding her round-up by period and genre are several sections on the obstacles women painters faced--the various constraints of family, love, ""poisonous praise,"" intimations of immorality, smallness of scale (i.e., lack of greatness) -- and these are a blend of the obvious, the arbitrary, and the speculative. It is hardly news today that artistically adept women were exploited by their painter fathers/husbands/lovers; or that they customarily adopted -- or aped -- their mentors' styles. (The sexual politics of the Walter Sickert and Augustus John circles are, nonetheless, intriguing.) Nor are we surprised to hear that women painters were patronized (in either sense) as prodigies; and it is easy to believe that their reputations were sometimes unjustly sullied -- as were other women's, painters or not. Greer is most impressive, in fact, when she discusses those rebels who were not cowed by the assorted obstacles -- Suzanne Valadon, Romaine Brooks, or that ""Magnificent Exception"" Artemisia Gentileschi (1593?-1653), to whom Greer devotes a chapter. Otherwise this is a contribution to feminist history but not to the history of art.