The eruption of big data with the increasing collection and processing of vast volumes and variety of data have led to breakthrough discoveries and innovation in science, engineering, medicine, commerce, criminal justice, and national security that would not have been possible in the past. While there are many benefits to the collection and usage of big data, there are also growing concerns among the general public on what personal information is collected and how it is used. In addition to legal policies and regulations, technological tools and statistical strategies also exist to promote and safeguard individual privacy, while releasing and sharing useful population-level information. In this overview, I introduce some of these approaches, as well as the existing challenges and opportunities in statistical data privacy research and applications to better meet the practical needs of privacy protection and information sharing.