Recently, there has been a growing debate over approaches for handling and analyzing private data. Research has identified issues with syntactic approaches such as k-anonymity and l-diversity. Differential privacy, which is based on adding noise to the analysis outcome, has been promoted as the answer to privacy-preserving data mining. This paper looks at the issues involved and criticisms of both approaches. We conclude that both approaches have their place, and that each approach has issues that call for further research. We identify these research challenges, and discuss recent developments and future directions that will enable greater access to data while improving privacy guarantees.