Recent commissioning of high-resolution spectropolarimeters capable of recording stellar spectra in all four Stokes parameters has led to a major improvement in our understanding of the structure and evolution of stellar magnetic fields. Rotationally modulated linear polarization in spectral lines has been detected for a number of early- and late-type magnetic stars. We have developed magnetic Doppler imaging codes capable of inverting these data into 2D maps of vector magnetic field and horizontal inhomogeneities of temperature and chemical abundance. This magnetic tomography method has been applied to Stokes vector observations of a sample of bright Ap stars, yielding the first robust assumption-free stellar magnetic field maps. Magnetic images reveal significant local deviations of the field geometry from a low-order multipolar structure, which were completely unexpected based on earlier modelling limited to intensity and circular polarization. This discovery has important implications for theories explaining the origin and evolution of fossil fields in Ap stars. High resolution magnetic maps also provide an important new observational constraint for theoretical investigation of complex interaction between magnetic field, radiatively-driven diffusion and magneto-acoustic pulsations.