This feature article is derived from the author's presentation of the Lonsdale lecture at the BCA Spring Meeting in 2018. One of the research results for which Kathleen Lonsdale is best known was her 1929 demonstration that the benzene ring in crystalline hexamethylbenzene is planar and has essentially hexagonal symmetry, resolving decades of dispute among organic chemists. More recent crystallographic studies of hexamethylbenzene have shown that there are actually small deviations from planarity. Such deviations for aromatic compounds may be due to electronic, steric, and/or intermolecular factors. Some substituted benzene molecules display remarkably large deviations, both from a planar ring structure and from regular hexagonal angular geometry around the ring. Starting from this specific connection with Kathleen Lonsdale's research, a number of stories are recounted of structural distortions and deviations from expected results and explanations that have been suggested for them, across a wide range of chemical topics including macrocycles, metal clusters, unusual coordination geometry and isomerism. On the way we find genuine surprises and results that have led to new understanding, but also examples of poor experiments, misinterpretation of data, scientific bias and preconceived ideas, incompetence and even deliberate fraud. Some aspects of structure validation are discussed. While showcasing some interesting research in its own right, this account also serves an educational purpose.