  At a generic quantum critical point, the thermal expansion $\alpha$ is more
singular than the specific heat $c_p$. Consequently, the "Gr\"uneisen ratio'',
$\GE=\alpha/c_p$, diverges. When scaling applies, $\GE \sim T^{-1/(\nu z)}$ at
the critical pressure $p=p_c$, providing a means to measure the scaling
dimension of the most relevant operator that pressure couples to; in the
alternative limit $T\to0$ and $p \ne p_c$, $\GE \sim \frac{1}{p-p_c}$ with a
prefactor that is, up to the molar volume, a simple {\it universal} combination
of critical exponents. For a magnetic-field driven transition, similar
relations hold for the magnetocaloric effect $(1/T)\partial T/\partial H|_S$.
Finally, we determine the corrections to scaling in a class of metallic quantum
critical points.
