The study of the conformation properties of macromolecules is at the heart of polymer science. Essentially all physical properties of polymers are manifestations of the underlying polymer conformations or otherwise significantly impacted by the conformation properties. In this Perspective, we review some of the key concepts that we have learned over nearly eight decades of the subject and outline some open questions. The topics include both familiar subjects in polymer physics textbooks and more recent results or not-so-familiar subjects, such as non-Gaussian chain behavior in polymer melts and topological effects in ring polymers. The emphasis is on understanding the key concepts, with both physical reasoning and mathematical analysis, and on the interconnection between the different results and concepts.