A theoretical basis for the embryology of conjoined twins was formulated from clinical experience with ten cases and extensive review of pertinent embryologic and clinical literature, including over 500 cases. Regarding the age old question of fusion or fission, it is concluded that there is no known embryologic process by which conjoined twins can be formed by fission but firm evidence to support fusion in all cases. Whether the fusion occurs between embryos on one embryonic disc or on two is of no consequence since they are all monovular. Intact ectoderm will not fuse to intact ectoderm, and all seven types of conjoined twins are explained by seven possible sites of union in the early embryo. One new term is proposed: parapagus, from the Greek para, meaning "side," combined with pagus, meaning "fixed"; this is the group formerly called dicephalus or diprosopos. These anterolaterally united parapagus twins must result from two nearly parallel notochords in close proximity; craniopagi and pygopagi from fusion at the cranial and caudal neuropores, respectively; cephalopagi and ischiopagi from union at the pharyngeal and cloacal membranes, respectively; thoracopagi from merging of the cardiac anlage; and omphalopagi from fusion of the umbilicus or of the edges of two embryonic discs in any area not including the above sites. Parasitic twins result from embryonic death of one twin, leaving various portions of the body vascularized by the surviving autosite. The rarity of cases (2) not easily explained by the above theories, and the nearly 6% of twins with two umbilical cords arising from the placenta would seem to support these conclusions. Should one wish to learn the methods of a conjurer, he might vainly watch the latter's customary repertoire, and, so long as everything went smoothly, might never obtain a clue to the mysterious performance, baffled by the precision of the manipulations and the complexity of the apparatus; if, however, a single error were made in any part or if a single deviation from the customary method should force the manipulator along an unaccustomed path, it would give the investigator an opportunity to obtain a part or the whole of the secret.(ABSTRACT TRUNCATED AT 400 WORDS)