This paper reviews the recent advances in computing coseismic deformations,and their contributions to seismology and geodesy. At first,an overview on the history of the dislocation theory development is given in the introduction section. Then,emphasis are given on some new developments through few examples in the following sections,such as the new dislocation theory for a 3D Earth model,a new computing scheme on coseismic deflection change of vertical,the relation of dislocation Love number and the conventional Love numbers,the application of dislocation theory applied in satellite gravity observations,the coseismic deformations observed by GRACE,and a new method to determine dislocation Love numbers by GRACE. Furthermore,some advanced theoretical and cases studies are introduced to illustrate how dislocation theory is important in interpret geodetic data,or invert seismic slip for co- and post-seismic processes,using seismic and geodetic data. Final remarks are given in the last section,with discussions,conclusions,comments on existing problems,and expected methods to solve them. This paper reviews the recent advances in computing coseismic deformations, and their contributions to seismology and geodesy. Then first, an overview on the history of the dislocation theory development is given in the introduction section. Then, emphasis are given on some new developments through few examples in the following sections, such as the new dislocation theory for a 3D Earth model, a new computing scheme on coseismic deflection change of vertical, the relation of dislocation Love number and the conventional love numbers, the application of dislocation theory applied in satellite gravity observations, the coseismic deformations observed by GRACE, and a new method to determine dislocation Love numbers by GRACE. Furthermore, some advanced theoretical and case studies are introduced to illustrate how dislocation theory is important in interpreting geodetic data, or invert seismic slip for co- and post-seismic processes, using seismic and geodetic data. Final remarks are given in the last secti on, with discussions, conclusions, comments on existing problems, and expected methods to solve them.