The transfer of electrons in molecules and solids is an essential process both in biological systems and in electronic devices. Devices that take advantage of the unique electronic properties of a single molecule have attracted much attention, and applications of these devices include molecular wire, molecular memory, and molecular diodes. The so-called Landauer formula with Green's function techniques provides a basis for theoretical calculations of coherent electron transport in metal-molecule-metal junctions. We have developed a chemical way of thinking about electron transport in molecules in terms of frontier orbital theory. The phase and amplitude of the HOMO and LUMO of π-conjugated molecules determine the essential properties of their electron transport. By considering a close relationship between Green's function and the molecular orbital, we derived an orbital rule that would help our chemical understanding of the phenomenon. First, the sign of the product of the orbital coefficients at sites r and s in the HOMO should be different from the sign of the product of the orbital coefficients at sites r and s in the LUMO. Second, sites r and s in which the amplitude of the HOMO and LUMO is large should be connected. The derived rule allows us to predict essential electron transport properties, which significantly depend on the route of connection between a molecule and electrodes. Qualitative analyses of the site-dependent electron transport in naphthalene (as shown in the graphics) demonstrate that connections 1-4, 1-5, 2-3, and 2-6 are symmetry-allowed for electron transmission, while connections 1-8 and 2-7 are symmetry-forbidden. On the basis of orbital interaction analysis, we have extended this rule to metal-molecule-metal junctions of dithiol derivatives in which two gold electrodes have direct contacts with a molecule through two Au-S bonds. Recently we confirmed these theoretical predictions experimentally by using nanofabricated mechanically controllable break junctions to measure the single-molecule conductance of naphthalene dithiol derivatives. The measurement of the symmetry-allowed 1,4-naphthalene dithiol shows a single-molecule conductance that exceeds that of the symmetry-forbidden 2,7-naphthalene dithiol by 2 orders of magnitude. Because the HOMO and LUMO levels and the HOMO-LUMO gaps are similar in the derivatives, the difference in the measured molecular conductances arises from the difference in the phase relationship of the frontier orbitals. Thus, the phase, amplitude, and spatial distribution of the frontier orbitals provide a way to rationally control electron transport properties within and between molecules.