Abstract: Previous theoretical analyses have indicated that the tropics and the extratropics are relatively independent from each other due to the existence of the critical latitudes. However, a large number of observational evidences have shown that there exists an obvious dynamical linkage between the tropics and the mid-latitudes. To help people better understand the atmospheric teleconnections, several theories of wave energy propagation are reviewed based on large number of literatures. It is shown that: (1) The great circle theory reveals the characteristics of Rossby waves propagating in the spherical atmosphere; (2) the westerly duct theory suggests a "corridor" through which the mid-latitude disturbances in one hemisphere can propagate into the other hemisphere; (3) the theory of energy accumulation-wave emanation proposes the possible processes about how tropical disturbances affect the atmospheric motions in the higher latitudes; (4) the theory of wave swelling further explains the physical mechanism for tropical-extratropical interaction, and (5) the meridional basic flow theory argues that stationary waves can propagate across the tropical easterlies under certain conditions. Besides, the advances in diagnostics of wave-flow interaction, particularly for the Rossby wave, the inertial-gravity wave, and the Kelvin wave, are also reviewed. The meridional propagation of atmospheric energy exhibits significant annual and interannual variations, which are closely related with the ENSO events and variations of the westerly jets, tropical upper-troposphere troughs, and others.