Quarkonium production in CMS

This talk presents the J/$\psi$ differential cross sections in pp collisions at 7 TeV, as a function of transverse momentum and in several rapidity ranges, on the basis of the 2010 data collected by CMS. The B to J/$\psi$ fraction is also presented and compared to other measurements. We also report the measurement of the Upsilon(1S), Upsilon(2S), and Upsilon(3S) differential cross sections as a function of transverse momentum and rapidity. We conclude with an outlook for prospects with the 2011 data, including a measurement of the $\chi_c$ states.