Conventionally, in longitudinal studies, the mean structure has been thought
to be more important than the covariance structure between the repeated
measures on the same individual. Often, it has been argued that, with re-
spect to the mean, the covariance was merely a `nuisance parameter' and,
consequently, was not of `scientific interest'. Today, however, one can see
that from a formal statistical standpoint, the inferential problem is entirely
symmetric in both parameters. In recent years there has been a steady
stream of new results and we pause to review some key advances in the expanding field of covariance modelling, In particular, developments since the
seminal work by Pourahmadi (1999, 2000) are traced. While the main focus
is on longitudinal data with continuous responses, emerging approaches to
joint mean-covariance modelling in the GEE, and GLMM arenas are also
considered briefly
