  Thermodynamics unavoidably contains fluctuation theory, expressible in terms
of a unique thermodynamic information metric. This metric produces an invariant
thermodynamic Riemannian curvature scalar $R$ which, in fluid and spin systems,
measures interatomic interactions. Specifically, $|R|$ measures the size of
organized fluctuating microscopic structures, and the sign of $R$ indicates
whether the interactions are effectively attractive or repulsive. $R$ has also
been calculated for black hole thermodynamics for which there is no consensus
about any underlying microscopic structures. It is hoped that the physical
interpretation of $R$ in fluid and spin systems might offer insight into black
hole microstructures. I give a brief review of results for $R$ in black holes,
including stability, the sign of $R$, R=0, diverging |R|, and various claims of
"inconsistencies" in thermodynamic metric geometry.
