The charge density wave ground state develops in low-dimensional metals as a consequence of electron-phonon interactions. The description of the electron-phonon interaction is usually referred to as a rigid ion approximation: it is assumed that the ionic potential V at any point depends only on the distance from the center of the ion. The formalism which has been developed for single particle tunneling in superconductors can be adopted to describe the occurrence of tunneling in the charge density wave ground state. The second order phase transition which leads to the charge density wave ground state has been examined by measurements of various thermodynamic quantities such as specific heat, thermal expansion, and elastic constants. Charge density waves have also been observed by scanning tunneling microscopy in various materials. In addition to normal metal-charge density wave tunneling, it is expected that other tunneling phenomena, such as charge density wave-charge density wave tunneling and phonon structures may also be observed.