Differential Higgs + jet production in bottom quark annihilation and gluon fusion

We present recent developments concerning Higgs production in bottom quark annihilation and gluon fusion. For bottom quark annihilation, we show the transverse momentum distribution of the associated jets. Furthermore, we discuss the distribution of events into n-jet bins for n=0 and n>0 at NNLO and NLO, respectively. For gluon fusion, the quality of the heavy-top limit for differential quantities at O(αs4) is studied by taking into account higher order terms in the 1/mtop expansion.