Digital image forensics is a relatively new research field that aims to expose the origin and composition of, and the history of processing applied to digital images. Hence, the digital image forensics is expected to be of significant importance to our modern society in which the digital media are getting more and more popular. In this thesis, image tampering detection and classification of double JPEG compression are the two major subjects studied. Since any manipulation applied to digital images changes image statistics, identifying statistical artifacts becomes critically important in image forensics. In this thesis, a few typical forensic techniques have been studied. Finally, it is foreseen that the investigations on endless confliction between forensics and anti-forensics are to deepen our understanding on image statistics and advance civilization of our society.