Rapid progress of nanotechnology requires developing novel theoretical methods to explain complicated experimental results and predict new functions of nanodevices. Thus, for the last decade, one of the challenging works of quantum chemistry is to understand the electron and spin transport phenomena in molecular devices. This critical review provides an extensive survey of on-going research and its current status in molecular electronics with the focus on theoretical applications to diverse types of devices along with a brief introduction of theoretical methods and its practical implementation scheme. The topics cover diverse molecular devices such as molecular wires, rectifiers, field effect transistors, electrical and optical switching devices, nanosensors, spin-valve devices, negative differential resistance devices and inelastic electron tunnelling spectroscopy. The limitations of the presented method and the possible approaches to overcome the limitations are addressed (183 references).