In this work, the ability of two non-covalent directional interactions (halogen and hydrogen bonds) to influence the structure of self-assembled physisorbed organic monolayers is considered. These layers exhibit only weak, non-directional interactions with the substrate, and so their structure is driven by the adsorbate-adsorbate interactions. In the initial phase of work, scanning tunnelling microscopy (STM) images of perylene tetracarboxylic diimide on a gold {111} surface are collected, exhibiting an unprecedented level of sub-molecular resolution of the structural detail of the molecular monolayer. In addition to this, a novel monolayer phase of 4,4-bipyridine is identified, and the difficulty of utilising halogen bonds for self assembly on a metallic surface demonstrated. The major technique used in this work is powder X-ray diffraction of monolayers deposited on a recompressed graphite surface. A novel scattering geometry and the use of a 2D area detector has allowed the collection of near-synchrotron-quality diffractograms using a lab based rotating anode X-ray source within a reasonable timeframe. Using this technique it has been possible to characterise the assembly of a range of pure adsorbed monolayers, and a number of co-crystalline monolayers. 1,3,5-triiodotrifluorobenzene was successfully characterised both alone, and upon co-deposition with 4,4’-bipyridine and s-triazine. It has also been possible to demonstrate the assembly of a homologous series of co-crystals between various α,ω-diiodinated perfluoroalkanes and 4,4’-bipyridine. All of the above systems have been structurally characterised for the first time. Importantly, for several of these key systems the experimental structures have been used to allow collaborators to theoretically simulate the layers using DFT. This DFT work provides a more detailed, quantitative understanding of the key factors determining the structure of these novel halogen-bonded monolayers, particularly the relative importance of the halogen bonding and van-der Waals forces. This balance of forces is used to discuss the long-term aim of designing porous monolayer systems. In addition to the above, a parallel stream of work considers the assembly of trimesic acid on graphite. This system has been explored by others using STM, however the quantitative details of the lattice constant, and the reality of the coexistence of two monolayer phases has until now been uncertain. Very significant experimental challenges have been overcome in this work, particularly depositing monolayer samples of the trimesic acid, to successfully determine diffraction patterns. These patterns allow calculation of the lattice constants of the “flower” and “chickenwire” phases, and to estimate the relative proportions of each. These experiments provide a demonstration of the utility of XRD as a complementary technique to STM for study of systems such as these.