Data science holds incredible promise of improving people's lives, accelerating scientific discovery and innovation, and bringing about positive societal change. Yet, if not used responsibly, this technology can generate economic inequality, destabilize global markets and worsen systemic bias. We consider issues such as bias and violation of data privacy in data analysis. We discuss desirable properties of data analysis such as fairness, transparency, neutrality, and diversity. Our goal is to draw the attention of the computer science community to the important emerging subject of responsible data management and analysis. We present our perspective on the issue, and motivate research directions. The data management research field has traditionally been driven primarily by enterprise data and focused on developing more and more sophisticated data models, and tackling issues such as performance and reliability. We believe that, in the future, the field will be increasingly driven by personal and social data, and will need to deal with challenging ethical issues. We will have to design concepts and principles to guide us in determining which behaviors, in data management, help us and which are harmful. To move computer science towards more responsible data analysis, the first issue is that of specifying desired properties. To make it operational in computers automatic decisions, the policy has to be made precise, to be formally stated in technical language. The computers role is also to help control the properties of data analysis by providing: tools to collect and analyze data responsibly, and tools to verify that data analysis was performed responsibly. To check the behavior of a program, one can either analyze its code (in the style of proving mathematical theorems) or test its effect (in the style of the experimental study of phenomena such as climate or the human heart). Both approaches have been intensely investigated, e.g., for guaranteeing security or performance, but much less for enforcing ethical properties such as fairness.