The structural complexity of many natural products sets them apart from common synthetic drugs, allowing them to access a biological target space that lies beyond the enzyme active sites and receptors targeted by conventional small molecule drugs. Naturally occurring cyclic peptides, in particular, exhibit a wide variety of unusual and potent biological activities. Many of these compounds penetrate cells by passive diffusion and some, like the clinically important drug cyclosporine A, are orally bioavailable. These natural products tend to have molecular weights and polar group counts that put them outside the norm based on classic predictors of "drug-likeness". Because of their size and complexity, cyclic peptides occupy a chemical "middle space" in drug discovery that may provide useful scaffolds for modulating more challenging biological targets such as protein-protein interactions and allosteric binding sites. However, the relationship between structure and pharmacokinetic (PK) behavior, especially cell permeability and metabolic clearance, in cyclic peptides has not been studied systematically, and the generality of cyclic peptides as orally bioavailable scaffolds remains an open question. This review focuses on cyclic peptide natural products from a "structure-PK" perspective, outlining what we know and don t know about their properties in the hope of uncovering trends that might be useful in the design of novel "rule-breaking" molecules.