  We report on long-term multi-wavelength monitoring of blazar Mrk 421 by the
GASP-WEBT collaboration and Steward Observatory, and by the Swift and Fermi
satellites. 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 show
fair correlation with the optical ones starting from 2012. We analyse
spectropolarimetric data and find wavelength-dependence of the polarisation
degree (P), which is compatible with the presence of the host galaxy, and no
wavelength-dependence of the electric vector polarisation angle (EVPA). Optical
polarimetry shows a lack of simple correlation between P and flux and wide
rotations of the EVPA. We build broad-band spectral energy distributions with
simultaneous near-infrared and optical data from the GASP-WEBT and UV and X-ray
data from the Swift satellite. They show strong variability in both flux and
X-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 variability
is compatible with jet models including at least two emitting regions that can
change their orientation with respect to the line of sight.
