Planar cell polarity (PCP) is a small but important area of research. In this review we discuss a limited number of topics within the PCP field, chosen because they are difficult, unsolved, controversial or just because we find them interesting. Because Drosophila is the best studied and technically most amenable system we have concentrated on it, but also consider some examples from work on vertebrates. Topics discussed include the number of genetic pathways involved in PCP, as well as the causal relationship between embryonic axes, gradients of morphogens and PCP itself. We consider the vexed question of the roles of the Wnt genes in PCP in both vertebrates and Drosophila. We discuss whether the proteins involved in PCP need to be localised asymmetrically in cells in order to function. We criticise the way the Hippo pathway is described in the literature and ask what its wildtype function is. We explore afresh how the Hippo pathway might be linked both to growth and to PCP through the gigantic cadherin molecule Fat. We offer some new ways of making sense of published results, particularly those relating to the Frizzled/Starry night and Dachsous/Fat systems of PCP.