Privacy has been a hot issue since early 2000s, in particular with the rise of social network and data outsourcing. Data privacy is a big concern in data outsourcing because it involves sharing personal data with third parties. In this talk, I will give an introduction to data privacy on topics such as privacy standards, data anonymization techniques, and data anonymization usage in data outsourcing and data mining. Then, I will present our work in data mining using anonymized data. We propose a data publisher-third party decision tree learning method for outsourced private data. The privacy model is anatomization/fragmentation: the third party sees data values, but the link between sensitive and identifying information is encrypted with a key known only to data publisher. Data publishers have limited processing and storage capability. Both sensitive and identifying information thus are stored on the third parties. The approach presented also retains most processing at the third parties, and data publisher-side processing is amortized over predictions made by the data publishers. Experiments on various datasets show that the method produces decision trees approaching the accuracy of a non-private decision tree, while substantially reducing the data publisher's computing resource requirements.