CONSPECTUS: The arrangement of molecular species into extended structures remains the focus of much current chemical science. The organization of molecules on surfaces using intermolecular interactions has been studied to a lesser degree than solution or solid-state systems, and unanticipated observations still lie in store. Intermolecular hydrogen bonds are an attractive tool that can be used to facilitate the self-assembly of an extended structure through the careful design of target building blocks. Our studies have focused on the use of 3,4,9,10-perylene tetracarboxylic acid diimides (PTCDIs), and related functionalized analogues, to prepare extended arrays on surfaces. These molecules are ideal for such studies because they are specifically designed to interact with appropriate diaminopyridine-functionalized molecules, and related species, through complementary hydrogen bonds. Additionally, PTCDI species can be functionalized in the bay region of the molecule, facilitating modification of the self-assembled structures that can be prepared. Through a combination of PTCDI derivatives, sometimes in combination with melamine, porous two-dimensional arrays can be formed that can entrap guest molecules. The factors that govern the self-assembly processes of PTCDI derivatives are discussed, and the ability to construct suitable target arrays and host-specific molecular species, including fullerenes and transition metal clusters, is demonstrated.