Abstract: Lithospheric rheological structure is a key factor in controlling lithosphere deformation in different tectonic environments. With the development of space geodetic observation techniques in recent years, postseismic deformation studies based on space geodetic observations have been used to infer mechanical properties of fault zones and lithospheric rheological structure. Firstly, we introduce the tectonophysical background of afterslip and distributed ductile flow from the associated friction and rheological experiments, respectively, and summarize the developments of numerical models and constitutive laws for postseismic deformation studies. The numerical models include analytical, semi-analytical, and purely numerical models, whose constitutive laws involve rate-and-state friction afterslip, standard linear rheological models (e.g., Maxwell body and standard linear solid) and transient rheological models (e.g., macroscopic and empirically derived Burgers body and microscopic power-law flow) of distributed ductile flow. Then, we review the development of postseismic deformation studies from case studies associated with the 1992 M_W7.3 Landers and 1999 M_W7.1 Hector Mine earthquakes in southern California, USA. Finally, we review recent advances on the lithospheric rheological structure studies and show how challenging the studies on the lithospheric rheological structure are by the controversial Jelly Sandwich and Crème Br?léé rheological models in postseismic deformation studies.