Most of today's software users interact with the software through a graphical user interface (GUI), which constitutes as much as 45-60% of the total code. The correctness of the GUI is necessary to ensure the correctness of the overall software. Although GUIs have become ubiquitous, testing GUIs for functional correctness has remained a neglected research area. Existing GUI testing techniques are extremely resource intensive primarily because GUIs have very large input spaces and evolve frequently. This dissertation overcomes the limitations of existing techniques by developing a process with supporting models, techniques, and tools for continuous integration testing of evolving GUI-based applications. The key idea of this process is to create three concentric testing loops, each with specific GUI testing goals, resource usage, and targeted feedback. The innermost fully automatic loop called crash testing operates on each code change of the GUI software. The second semi-automated loop called smoke testing operates on each day's GUI build. The outermost loop called comprehensive GUI testing is executed after a major version of the GUI is available. The primary enablers of this process, also developed in this dissertation, include an abstract model of the GUI and a set of model-based techniques for test-case generation, test oracle creation, and continuous GUI testing. The model and techniques were obtained by studying GUI faults, interactions between GUI events, and why certain event interactions lead to faults. The continuous testing process and associated techniques are shown to be useful, via several large experiments involving millions of test cases, on both in-house and open-source GUI applications.