Modelling of magnetic Ap type stars has a long and distinguished history. The Oblique Rotator Model (ORM) – a dipole inside the star, its axis not aligned with the rotation axis – proposed by Babcock (1949a) provides a simple yet flexible enough paradigm for the modelling both of the magnetic and the spectral line variations of these stars. Deutsch (1958) developed a method to derive surface composition distributions from magnetic field measurements in conjunction with line strength variations but subsequent investigators concentrated either on the magnetic field or on the abundance distributions. Hardly ever was the question of consistency between field and composition mapping addressed – Landstreet (1988) constitutes the exception. In abundance mapping, Doppler imaging (Vogt et al. 1987) has meanwhile replaced most other approaches and is credited with fairly reliable results. But can one really carry out such mapping, as done by Hatzes (these proceedings) without accounting for the magnetic field and can these zero-field abundance maps and their relation to the magnetic configuration be compared to the predictions of diffusion theory? Did Landstreet ever have a real chance of disentangling magnetic and abundance effects using intensity (Stokes I) profiles only? What is the probability of obtaining spurious surface structure from intensity Doppler imaging of Ap stars?