Abstract: Studies on cases of more than 10 strong earthquakes of M6.0 to M9.0 since the 2008 Wenchuan earthquake around the world with GPS observations and crustal deformation precursors are reviewed. These earthquakes occurred in regions of different tectonic movements and of different types. They are the M8.0 Wenchuan earthquake in 2008, the M9.0 Tohoku earthquake in 2011 in Japan, the M7.0 Lushan earthquake in 2013 and so on until the recent earthquake of M7.4 in Mexico in Jun., 2020 and the southern Alaska offshore earthquake of M7.8 in Jul., 2020. Based on the time series of horizontal displacement components and horizontal displacement field, particularly the time series of horizontal displacement vectors, in the regional reference frames, studies have shown that the coseismic displacements are the keys to the confirmation of the existence of crustal deformations precursory to earthquakes. The time series of vertical displacements and horizontal displacement vectors, the coseismic vertical displacements and decomposition of the coseismic horizontal displacement vectors have revealed the real pattern of elastic rebound. A model of rebound or elastic rebound of (preseismic) compression-(coseismic) shear strain is proposed in agreement with results of rock failure tests and the GPS observations. Based on the studies of the earthquake cases, a layout of stations of continuous GNSS observations of monitoring precursory crustal deformations for possible predictions of earthquakes of different magnitudes is proposed.