Current information technology enables many organizations to collect, store, and use massive amount and various types of information about individuals. While sharing such a wealth of information presents enormous opportunities for data mining applications, data privacy has been a major barrier. Differential privacy is widely accepted as one of the strongest privacy guarantees. While many effective mechanisms have been proposed for specific data mining applications, non-interactive data release to support exploratory data analysis with differential privacy remains an open problem. I will present our Adaptive Differentially Private Data Release (ADP) project which aims to build a suite of data-driven and adaptive techniques for differentially private data release by exploiting the characteristics of the underlying data. I will present our ongoing work on techniques for handling different types of data including relational, high dimensional, transactional, sequential, and time series data. I will present case studies using real datasets demonstrating the feasibility of using the released data for various data mining tasks such as classification and frequent pattern mining. Finally, I will discuss the challenges and open questions of applying the differential privacy framework for general data sharing.