The interaction of molecules with intense low-frequency laser pulses is a rapidly developing field attracting much theoretical and experimental interests. One of the main goals is to establish techniques for retrieving the molecular structure information from experimental observables. The retrieving procedure requires the knowledge of the tunneling ionization rate of a target molecule. This important characteristic of the first step of the interaction process depends on the internuclear configuration and the symmetry of an ionizing orbital which are revealed in its dependence on the orientation of a molecule with respect to the laser field. Recently we have developed a new theory of tunneling ionization of atoms and molecules based on the Siegert states which are the solutions to the Schrodinger equation satisfying the outgoing boundary condition and regularity. In this talk, we will present basics of the theory as well as some applications.