While there has been significant progress in the theory and practice in data science in recent years, many fundamental challenges remain. Some are mathematical in nature, such as the challenges associated with optimization and sampling in high-dimensional spaces. Some are statistical in nature, including the challenges associated with multiple decision-making. Others are economic in nature, including the need to take scarcity into account, and to provide services and incentives in data-based markets. And others are systems challenges, arising from the need for highly-scalable, robust and understandable hardware and software platforms. I will overview these challenges, and discuss recent progress.