We update the theoretical predictions for direct Upsilon(nS) hadroproduction in the framework of nonrelativistic QCD. We show that the next-to-leading order corrections in alpha(S) to the color-singlet transition significantly raise the differential cross section at high p(T) and substantially affect the polarization of the Upsilon. Motivated by the remaining gap between the next-to-leading order yield and the cross-section measurements at the Fermilab Tevatron, we evaluate the leading part of the alpha(S)(5) contributions, namely, those coming from Upsilon(nS) associated with three light partons. The differential color-singlet cross section at alpha(S)(5) is in substantial agreement with the data, so that there is no evidence for the need of color-octet contributions. Furthermore, we find that the polarization of the Upsilon(nS) is longitudinal. We also present our predictions for Upsilon(nS) production at the LHC.