Vivian's books, articles, and reviews have covered the history of medicine from Antiquity to present. They have centred on the history of the classical tradition in medicine before 1650, and  particularly on the life, works and influence of Galen of Pergamum (129-ca. 216). He has also published extensively on the history of medicine in the fifteenth and sixteenth centuries, across Europe, in Wittenberg and Vienna as well as in Paris and Padua. More recently, he has written on the historiography of medicine in the nineteenth and twentieth centuries, in part as a result of his editorial work for the Rezeptions- und Wissenschaftsgeschichte volumes of Der neue Pauly.

The discovery in 2009 of Vesalius' own annotated copy of second edition of the De humani corporis fabrica, Basle 1555, opened a new phase in Vivian's research. Having first published a detailed study of these notes by the most famous of all anatomists (1514-1564), he was allowed in 2014 to see a further set of notes written into his 1538 Institutiones. He published a preliminary study in 2015, and in 2017 the first English translation, with notes, of the Institutiones, an unnoticed stage in the development of Vesalius's ideas. His most recent project is an annotated English translation of the auto-bibliography of the sixteenth-century English physician John Caius (1610-1573).

 In 2006 Vivian was awarded a major Wellcome grant for a project to edit some 80 unpublished medical papyri from greco-roman Egypt. Having fulfilled the initial brief to draw up a preliminary handlist, he handed leadership of the project to Dr. N. Gonis, UCL, on retirement, but remained actively involved and co-ordinated the team of papyrologists until the project was published in 2014..