The components of petroleum asphaltenes exhibit complex bridged structures comprising sulfur, nitrogen, aromatic, and naphthenic groups linked by alkyl chains. These components aggregate in crude oil and toluene over a wide range of concentrations and temperatures, exhibit strong adhesion to a wide range of surfaces, occlude components that are otherwise soluble, are porous to solvents, and are elastic under tension. None of these properties is consistent with an architecture dominated only by aromatic stacking by electrostatic and/or van der Waals forces, often called pi-pi stacking. We propose an alternate paradigm based on supramolecular assembly of molecules, combining cooperative binding by Bronsted acid-base interactions, hydrogen bonding, metal coordination complexes, and interactions between cylcoalkyl and alkyl groups to form hydrophobic pockets, in addition to aromatic pi-pi stacking. A range of architectures are suggested, which almost certainly occur simultaneously, including porous networks and host-guest complexes. The latter may include organic clathrates, in which occluded guest molecules stabilize the assembly of a cage, as methane does in gas hydrates. This model has a number of implications for analysis of asphaltene mixtures and predicting asphaltene phase behavior and transport properties.