In recent years, learning with weak supervision has become one of the hot research topics in machine learning. As one of the important weakly-supervised machine learning frameworks, partial label learning has been successfully applied to a number of real-world applications. In partial label learning, each object is described by a single instance (feature vector) in the input space. On the other hand, it is associated with a set of candidate labels among which only one is valid. The state-of-the-art on partial label learning researches is reviewed. Firstly, the problem definition on partial label learning as well as its differences and similarities with other related learning frameworks are given. Thenseveral representative partial label learning algorithms along with one of our recent progress on this topic are introduced. Finally, possible future investigations on partial label learning are briefly discussed.