A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. HAZEL is a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 1083.0 nm and 587.6 nm (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods.