In this era of miniaturized devices, there has been a huge number of experiments on transport through molecules and quantum dots. In this context, I shall discuss some basic mechanisms of how the current flows through a system with one level to many levels and the fundamental theories (like, Landauer and Buttiker formalisms), which predicted one-electron tunneling mechanisms and later some experiments which  verified those predictions. Recent developments in computer codes, through which one can predict various features of molecular current-voltage characteristics will be discussed. Current constraint approach and the rate equation method, which is required in Coulomb blockade regime of transport will be discussed. I shall also briefly discuss the recent advances in this field, i.e., tunneling due to inelastic scattering; light quanta assisted tunneling mechanisms; complete destruction of coherent tunneling and molecular field-effect transistors.