An important aspect of geometric morphometrics, since its beginnings, was the visualization of shape changes. A range of methods has been developed with advances in statistical shape analysis and new possibilities in computer graphics. Most approaches are based either on relative shifts of landmark positions in starting and target shapes after superimposition or on D’Arcy Thompson’s idea of transformation grids. Both approaches are in wide use in current morphometrics, and both have their distinctive advantages and shortcomings. This paper discusses the assumptions and some caveats of both approaches. The paper also offers some recommendations for authors of geometric morphometric studies.