We investigate the properties of Heisenberg S=1 chains with biquadratic interactions in magnetic fields. Extensive DMRG calculations reveal remarkable phase transitions between different types of Luttinger liquids. For negative biquadratic interactions, we identify a line of continuous phase transitions with central charge c=3/2 between two critical Luttinger liquid phases with central charge c=1: a phase with dominant transverse spin correlations is connected to a phase with dominant spin-nematic, quadrupolar correlations. For positive values of the biquadratic interactions, we find a pronounced kink-anomaly in the magnetization curve, which we identify as a transition between a two-component Luttinger liquid and a one-component Luttinger liquid phase at finite magnetization, ruling out an alternative scenario proposing vector chiral order.