  Various massive gravity theories in three dimensions are conjecturally dual
to logarithmic conformal field theories (LCFTs). We summarise the status of
these conjectures. LCFTs are characterised by the values of the central charges
and the so-called "new anomalies". We employ a short-cut to calculate these new
anomalies in generalised massive gravity and in the recently proposed
higher-derivative gravity theories with holographic c-theorem. Both cases
permit LCFTs exhibiting intriguing features, like rank three Jordan cells or
non-zero central charges. Finally, as an example we discuss in some detail the
partially massless version of new massive gravity, a theory with several
special properties that we call "partially massless gravity".
