  We review some recent results that express or rely on the locality properties
of the dynamics of quantum spin systems. In particular, we present a slightly
sharper version of the recently obtained Lieb-Robinson bound on the group
velocity for such systems on a large class of metric graphs. Using this bound
we provide expressions of the quasi-locality of the dynamics in various forms,
present a proof of the Exponential Clustering Theorem, and discuss a
multi-dimensional Lieb-Schultz-Mattis Theorem.
