Abstract: We present the theory and methods of earthquake rupture process inversion by using seismic and geodetic data, and their applications to scientific researches and earthquake emergency responses. It is shown that the knowledge obtained from these studies has much improved our understanding of the complexities of the earthquake source and causative mechanism of the earthquake disaster, and is of important reference value in earthquake disaster mitigation such as rapid earthquake emergency response. Especially since the 2008 $M_{{\rm w}}7.9$ $(M_{{\rm S}}8.0)$ Wenchuan, Sichuan, earthquake, fast and routine determination of the earthquake rupture process has been performed for significant earthquakes ($M_{{\rm S}}\ge 6.5$ in China and $M_{{\rm S}}\ge 7.5$ worldwide), and the results obtained are timely reported to the authorities and released to the public on the web site. The time consumed by the inversion has been reduced from more than 5 hours in 2009 to approximately 1-3 hours at present. The timely released rupture model was routinely used by the China Earthquake Administration and other authorities during the earthquake emergency responses period for destructive earthquakes, such as the 2010 $M_{{\rm w}}6.9$ Yushu earthquake, the 2013 $M_{{\rm w}}6.6$ Lushan earthquake, the 2014 $M_{{\rm w}}6.1$ Ludian earthquake, and the 2015 $M_{{\rm w}}7.8$ Gorkha, Nepal, earthquake, among the others.