The remarkable performance of the o1 model in complex reasoning demonstrates that test-time compute scaling can further unlock the model's potential, enabling powerful System-2 thinking. However, there is still a lack of comprehensive surveys for test-time compute scaling. We trace the concept of test-time compute back to System-1 models. In System-1 models, test-time compute addresses distribution shifts and improves robustness and generalization through parameter updating, input modification, representation editing, and output calibration. In System-2 models, it enhances the model's reasoning ability to solve complex problems through repeated sampling, self-correction, and tree search. We organize this survey according to the trend of System-1 to System-2 thinking, highlighting the key role of test-time compute in the transition from System-1 models to weak System-2 models, and then to strong System-2 models. We also point out advanced topics and future directions.