A data object is usually represented by a single feature vector in traditional learning settings. Though such a formulation has achieved great success, its utility is limited in dealing with data objects involving complex semantics where one object can belong to multiple semantic categories simultaneously. For example, an image showing a lion besides an elephant can be recognized simultaneously as an image on lion, elephant, wild or even Africa; the text document “Around the World in Eighty Days” can be put into multiple categories such as scientific novel, Jules Verne´s writings or even books on traveling simultaneously; a web page introducing the Bird´s Nest Stadium can be categorized as a web page on Olympics, sports or even Beijing city, etc. Such data objects are ubiquitous in real applications and need to be tackled in learning tasks. In this talk we will introduce the MIML framework which has been shown promising for learning data objects with complex semantics.