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We report on long-term multi-wavelength monitoring of blazar Mrk 421 by theGASP-WEBT collaboration and Steward Observatory, and by the Swift and Fermisatellites. We study the source behaviour in the period 2007-2015,characterized by several extreme flares. The ratio between the optical, X-ray,and \gamma-ray fluxes is very variable. The \gamma-ray flux variations showfair correlation with the optical ones starting from 2012. We analysespectropolarimetric data and find wavelength-dependence of the polarisationdegree (P), which is compatible with the presence of the host galaxy, and nowavelength-dependence of the electric vector polarisation angle (EVPA). Opticalpolarimetry shows a lack of simple correlation between P and flux and widerotations of the EVPA. We build broad-band spectral energy distributions withsimultaneous near-infrared and optical data from the GASP-WEBT and UV and X-raydata from the Swift satellite. They show strong variability in both flux andX-ray spectral shape and suggest a shift of the synchrotron peak up to a factor$\sim 50$ in frequency. The interpretation of the flux and spectral variabilityis compatible with jet models including at least two emitting regions that canchange their orientation with respect to the line of sight.

Dissecting the long-term emission behaviour of the BL Lac object Mrk 421