  With the recent completion of NNNLO results, the perturbative description of
the $\Upsilon$ system has reached a very high level of sophistication. We
consider the non-perturbative corrections as an expansion in terms of local
condensates, following the approach pioneered by Voloshin and Leutwyler. The
leading order corrections up to dimension eight and the potential NLO
corrections at dimension four are computed and given in analytical form. We
then study the convergence of the expansion for the masses, the leptonic decay
rates and the non-relativistic moments of the $\Upsilon$ system. We demonstrate
that the condensate corrections to the $\Upsilon(1S)$ mass exhibit a region
with good convergence, which allows us to extract
$\overline{m}_b(\overline{m}_b) =
4214\pm37\,(\text{pert.})\,_{-22}^{+20}\,(\text{non-pert.})\text{ MeV}$, and
show that non-perturbative contributions to the moments with $n\approx10$ are
negligible.
