We review some of our recent experimental results on charge transport in organic nanostructures such as self-assembled monolayer and monolayers of organic semiconductors. We describe a molecular rectifying junction made from a sequential self-assembly on silicon. These devices exhibit a marked current-voltage rectification behavior due to resonant transport between the Si conduction band and the π molecule highest occupied molecular orbital of the π molecule. We discuss the role of metal Fermi level pinning in the current-voltage behavior of these molecular junctions. We also discuss some recent insights on the inelastic electron tunneling behavior of Si/alkyl chain/metal junctions.