Traditional methods of pattern classification and machine learning usually assume closed world: the input pattern falls within a fixed set of classes. However, in open world, the input pattern can be of either known or unknown classes, or be outlier. While in training, the data may emerge incrementally, and the new dataset contain samples or with known or unknown classes, either labeled or unlabeled, or be outlier. Such open-world learning scenario involves multiple challenges including out-of-distribution (OOD) detection, confidence estimation, unlabeled data exploitation, catastrophic forgetting and novel category discovery. The challenges are attacked by combining techniques such as generative modeling, regularization, knowledge distillation, and hybrid learning. This talk will outline the status of open-world pattern recognition, identify the main challenges of open-world learning and main strategies, and present some recent progress achieved in my group: open-set recognition, class-incremental learning, and generalized category discovery.