Earthquakes on major continental faults and subduction zones can be catastrophic, leading to severe damage, injuries, and casualties. Seismic and geodetic evidence shows that faults have heterogeneous degrees of locking, where earthquakes tend to occur on locked asperities and creeping patches do not accumulate interseismic strain. Accurately delineating the seismic and aseismic slip behavior on continental faults over the earthquake cycle is crucial for seismic hazard evaluation. In this dissertation, I use the space-geodetic Interferometric Synthetic Aperture Radar (InSAR) to study the crustal deformation during the co-, post- and interseismic period on faults in the Tibetan Plateau and San Francisco Bay Area. The first chapter introduces the context and gives an overview of the dissertation. In Chapter 2, I present the study of the co- and postseismic deformation of the 2017 Jiuzhaigou earthquake at the eastern boundary of the Tibetan Plateau. The Jiuzhaigou earthquake exhibits a strong shallow slip deficit (SSD) and has one of the lowest afterslip signals of recorded earthquakes (1%-3%). Such observations provide important implications for accommodations of fault strain in the shallow part of the crust and fault frictional properties. Ultimately, the SSD should be recovered through one or more earthquake cycles to maintain the conservation of the long-term slip. In Chapter 3, I show the analysis of the high-resolution interseismic deformation on the creeping Xianshuihe Fault at the eastern boundary of the Tibetan Plateau. A coupling model that characterizes the distribution of creep with depth is derived from the interseismic velocity map. The seismic potential of apparent rupture asperities along the Xianshuihe Fault is further refined by considering fault-crossing baseline data and the distribution of historical ruptures and microseismicity. In Chapter 4, I determine the interseismic deformation over the southern San Francisco Bay Area. I constrain the surface creep rates on Bay Area creeping faults (San Andreas, Calaveras, Sargent, and Quien Sabe Faults) using cross-fault InSAR timeseries differences. I examine the spatiotemporal distribution of fault creep and identify a multi-annual fault coupling increase 2016-2018 on the San Andreas and Calaveras Fault. Finally in Chapter 5, I explore a deep learning approach to mitigate the atmospheric noise contributions and better detect the transient fault creep signals in the InSAR timeseries. The deep learning method is a promising approach to stretch the limit of InSAR on crustal deformation observation, with higher temporal resolution and better accuracy.