Traditional intent classification models are based on a pre-defined intent set and only recognize limited in-domain (IND) intent classes. But users may input out-of-domain (OOD) queries in a practical dialogue system. Such OOD queries can provide directions for future improvement. In this paper, we define a new task, Generalized Intent Discovery (GID), which aims to extend an IND intent classifier to an open-world intent set including IND and OOD intents. We hope to simultaneously classify a set of labeled IND intent classes while discovering and recognizing new unlabeled OOD types incrementally. We construct three public datasets for different application scenarios and propose two kinds of frameworks, pipeline-based and end-to-end for future work. Further, We conduct exhaustive experiments and qualitative analysis to comprehend key challenges and provide new guidance for future GID research.