Self-assembled physisorbed monolayers consist of regular two-dimensional arrays of molecules. Two-dimensional self-assembly of organic and metal–organic building blocks is a widely used strategy for nanoscale functionalization of surfaces. These supramolecular nanostructures are typically sustained by weak non-covalent forces such as van der Waals, electrostatic, metal–ligand, dipole–dipole and hydrogen bonding interactions. A wide variety of structurally very diverse monolayers have been fabricated under ambient conditions at the liquid–solid and air–solid interface or under ultra-high-vacuum (UHV) conditions at the UHV–solid interface. The outcome of the molecular self-assembly process depends on a variety of factors such as the nature of functional groups present on assembling molecules, the type of solvent, the temperature at which the molecules assemble and the concentration of the building blocks. The objective of this review is to provide a brief account of the progress in understanding various parameters affecting two-dimensional molecular self-assembly through illustration of some key examples from contemporary literature.