Just how we discriminate between the different odours we encounter is notcompletely understood yet. While obviously a matter involving biology, the core issue isa matter for physics: what microscopic interactions enable the receptors in our noses-smallprotein switches—to distinguish scent molecules? We survey what is and is not known aboutthe physical processes that take place when we smell things, highlighting the difficultiesin developing a full understanding of the mechanics of odorant recognition. The maincurrent theories, discussed here, fall into two major groups. One class emphasises thescent molecule's shape, and is described informally as a "lock and key" mechanism. Butthere is another category, which we focus on and which we call "swipe card" theories:the molecular shape must be good enough, but the information that identifies the smellinvolves other factors. One clearly-defined "swipe card" mechanism that we discuss hereis Turin's theory, in which inelastic electron tunnelling is used to discern olfactant vibrationfrequencies. This theory is explicitly quantal, since it requires the molecular vibrations totake in or give out energy only in discrete quanta. These ideas lead to obvious experimentaltests and challenges. We describe the current theory in a form that takes into accountmolecular shape as well as olfactant vibrations. It emerges that this theory can explainmany observations hard to reconcile in other ways. There are still some important gapsin a comprehensive physics-based description of the central steps in odorant recognition. We also discuss how far these ideas carry over to analogous processes involving other smallbiomolecules, like hormones, steroids and neurotransmitters. We conclude with a discussionof possible quantum behaviours in biology more generally, the case of olfaction being justone example. This paper is presented in honour of Prof. Marshall Stoneham who passedaway unexpectedly during its writing.