The autonomous ordering and assembly of atoms and molecules on atomically well-defined surfaces allow creating a wide range of surface nanostructures, opening an alternative 'bottom-up' route to the traditional 'top-down' fabrication methods of the microelectronics industry now approaching their fundamental limits. This review summarises some recent efforts of our team to grow molecular arrays on metal, insulating or semiconductor surfaces. In a fundamental approach, two-dimensional surface arrays of nanometre size have been obtained under ultrahigh vacuum by evaporation of molecules, functionalised to favour the intermolecular links rather than molecule-substrate ones. Intermolecular links such as hydrogen bonds, covalent or coordination bonding were profitably used to create various molecular networks. Alternatively, we also investigated molecular self-assembly from the solution whose architectures are mainly fixed by the molecule-substrate adsorption forces. Molecular assemblies were characterised using Scanning Near-Field Microscopies (Scanning Tunnelling Microscopy, non-contact-Atomic Force Microscopy), whereas electronic and vibrational properties were investigated by surface spectroscopy such as Ultra-Violet and X-ray Photoelectron Spectroscopy, infrared or Surface-Enhanced Raman Spectroscopy.