We present an overview of various aspects of the self-assembly of organic monolayers on silicon substrates for molecular electronics applications. Different chemical strategies employed for grafting the self-assembled monolayers (SAMs) of alkanes having different chain lengths on native oxide of Si or on bare Si have been reviewed. The utility of different characterization techniques in determination of the thickness, molecular ordering and orientation, surface coverage, growth kinetics and chemical composition of the SAMs has been discussed by choosing appropriate examples. The metal counterelectrodes are an integral part of SAMs for measuring their electrical properties as well as using them for molecular electronic devices. A brief discussion on the variety of options available for the deposition of metal counterelectrodes, that is, soft metal contacts, vapor deposition and soft lithography, has been presented. Various theoretical models, namely, tunneling (direct and Fowler-Nordheim), thermionic emission, Poole-Frenkel emission and hopping conduction, used for explaining the electronic transport in dielectric SAMs have been outlined and, some experimental data on alkane SAMs have been analyzed using these models. It has been found that short alkyl chains show excellent agreement with tunneling models; while more experimental data on long alkyl chains are required to understand their transport mechanism(s). Finally, the concepts and realization of various molecular electronic components, that is, diodes, resonant tunnel diodes, memories and transistors, based on appropriate architecture of SAMs comprising of alkyl chains (sigma- molecule) and conjugated molecules (pi-molecule) have been presented.