  We embark upon a systematic investigation of operator space structure of
JC*-triples via a study of the TROs (ternary rings of operators) they generate.
Our approach is to introduce and develop a variety of universal objects,
including universal TROs, by which means we are able to describe all possible
operator space structures of a JC*-triple. Via the concept of reversibility we
obtain characterisations of universal TROs over a wide range of examples. We
apply our results to obtain explicit descriptions of operator space structures
of Cartan factors regardless of dimension.
