Terrestrial substorms have been studied for over four decades and our understanding about this phenomenon has improved through those studies. However, many issues regarding substorms are still controversial, especially the initiation mechanism of substorm onset. To understand the initiation mechanism, we have to first answer some important questions. What is the substorm expansion onset? What is the physics behind its phenomenological definition? Where does the initiation start? What is the relation of tail reconnection with near-Earth onsets? Where does tail reconnection occur? While one way to understand better the physics of substorms is to increase the number of spacecraft and the resolution of ground observations, another way is to compare substorm phenomena between different planets. In this study, we investigate the different phases of substorms both on the Earth and Jupiter. For Jovian dynamic event, we need to know if they are substorms? How are they driven? How can we better understand terrestrial substorms through studying Jovian substorms? We used Polar, GOES, Cluster and ground-station observations to study terrestrial substorms and used the Galileo observations to study Jovian dynamic events. A 3-day growth phase of Jovian substorm is discovered, which is also found driven by the internal processes including mass-loading at Io instead of the solar wind. This discovery establishes the substorm nature of those dynamics events which have counterparts of key elements of terrestrial substorms, including the connection of those events with the Jupiter's polar auroral activity. Near-planet dipolarization caused by the mid-tail reconnection is also investigated. In the near-Earth tail region, dipolarizations appear to be associated with mid-tail reconnections, near-tail flow braking and formation of substorm current wedge. In both magnetospheres, major onsets of substorms are found to be due to the major tail reconnection which can globally release the loaded energy and return the accumulated magnetic flux in magnetotails. This major change of magnetotail energy and flux status should be used to define the expansion onset of terrestrial substorms. Through comparison of dipolarizations on the geosynchronous orbit (GOES) and 9 R _E near-tail region (Polar), it is found that dipolarization region starts within a narrow region and then expands both in the radial and azimuthal directions. The near-Jupiter dipolarizations and plasmoids are used to infer the Jovian tail reconnection site and the most possible location of Jovian tail neutral point is found at the post-midnight sector and 80 R_J from the planet. It is also very found that the Jovian tail reconnection starts within a confined region and expands afterwards, which is consistent with the narrow width of initial near-Earth dipolarization region and suggests tail reconnection associated with substorms mostly starts from a neutral point instead of a neutral line.