As nucleic acid testing is playing a vital role in increasingly many research fields, the need for rapid on-site testing methods is also increasing. The test procedure often consists of three steps: Sample preparation, amplification, and detection. This review covers recent advances in on-chip methods for each of these three steps and explains the principles underlying related methods. The sample preparation process is further divided into cell lysis and nucleic acid purification, and methods for the integration of these two steps on a single chip are discussed. Under amplification, on-chip studies based on PCR and isothermal amplification are covered. Three isothermal amplification methods reported to have good resistance to PCR inhibitors are selected for discussion due to their potential for use in direct amplification. Chip designs and novel strategies employed to achieve rapid extraction/amplification with satisfactory efficiency are discussed. Four detection methods providing rapid responses (fluorescent, optical, and electrochemical detection methods, plus lateral flow assay) are evaluated for their potential in rapid on-site detection. In the final section, we discuss strategies to improve the speed of the entire procedure and to integrate all three steps onto a single chip; we also comment on recent advances, and on obstacles to reducing the cost of chip manufacture and achieving mass production. We conclude that future trends will focus on effective nucleic acid extraction via combined methods and direct amplification via isothermal methods.