Complexity is a term that is often invoked by those writing appreciatively about the taste, aroma/ bouquet, and/or flavor of food and drink. Typically, the term is used as though everyone knows what is being talked about. Rarely is any explanation given, and the discussion soon moves on to other topics. However, oftentimes it is not at all clear what, exactly, is being referred to. A number of possibilities are outlined here, including physical complexity at the level of individual molecules, at the level of combinations of molecules giving rise to a specific flavor profile (e.g., as in a glass of quality wine or a cup of specialty coffee), at the level of combinations of distinct ingredients/elements (e.g., as when composing a particularly intricate dish in a high-end restaurant, say, or when pairing food with wine), and/or the number of stimuli/steps involved in the process of creation. Of course, people might also be referring to some aspect of their perceptual experience, and one of the intriguing questions in this space concerns the nature of the relationship(s) between these different ways of conceptualizing complexity in the chemical senses. However, given that physical/ chemical and perceived complexity so often diverge, we argue that it is the latter notion, or rather inferred complexity, that is the most relevant when it comes to the chemical senses. Finally, we look at the role of expertise and review the evidence suggesting that inferred complexity can emerge either from a unitary taste experience that is judged to be complex, or from a tasting experience having multiple individuable elements.