The basic assumptions made in the interpretation of the anisotropy of magnetic susceptibility (AMS) of lava flows, dykes and other tabular intrusive rocks have changed with time. This paper presents a historical account of those changes. Because several aspects of the AMS of these types of rocks are still open to debate, the historical perspective helps us to appreciate better the limitations that had to be faced at different times, therefore providing some clues that can be used to solve such controversies. Also, by benefiting from hindsight it is possible to devise alternative approaches that can be employed to interpret the AMS of these types of rocks. Although some adjustments to current models will be made as new results become available, it seems that at present the main commponents of the basic model of AMS in lava flows and tabular intrusive rocks have been finally reached, leaving behind most of the apparent contradictions found in earlier works. This progress is undoubtedly an important advance in our understanding of the nature of AMS in general.