Context. The quasar 3C 279 is among the most extreme blazars in terms of luminosity and variability of flux at all wavebands. Its variations in flux and polarization are quite complex and therefore require intensive monitoring observations at multiple wavebands to characterise and interpret the observed changes.Aims. In this paper, we present radio-to-optical data taken by the WEBT, supplemented by our VLBA and RXTE observations, of 3C 279. Our goal is to use this extensive database to draw inferences regarding the physics of the relativistic jet.Methods. We assemble multifrequency light curves with data from 30 ground-based observatories and the space-based instruments SWIFT (UVOT) and RXTE, along with linear polarization vs. time in the optical R band. In addition, we present a sequence of 22 images (with polarization vectors) at 43 GHz at resolution 0.15 milliarcsec, obtained with the VLBA. We analyse the light curves and polarization, as well as the spectral energy distributions at different epochs, corresponding to different brightness states.Results. We find that the IR-optical-UV continuum spectrum of the variable component corresponds to a power law with a constant slope of -1.6, while in the 2.4-10 keV X-ray band it varies in slope from -1.1 to -1.6. The steepest X-ray spectrum occurs at a flux minimum. During a decline in flux from maximum in late 2006, the optical and 43 GHz core polarization vectors rotate by ~300°.Conclusions. The continuum spectrum agrees with steady injection of relativistic electrons with a power-law energy distribution of slope -3.2 that is steepened to -4.2 at high energies by radiative losses. The X-ray emission at flux minimum comes most likely from a new component that starts in an upstream section of the jet where inverse Compton scattering of seed photons from outside the jet is important. The rotation of the polarization vector implies that the jet contains a helical magnetic field that extends ∼20 pc past the 43 GHz core.