Robot-assisted technology is a modern medical research topic with significant importance. Robot-assisted needle puncture technology not only has important theoretical significance, but also can effectively improve the accuracy and quality of surgical operations in clinic. Therefore, it can be applied extensively in the field of minimally invasive surgery. In this paper, the state of the art in the field of robot-assisted puncture technology is introduced. Firstly, the existing robot-assisted puncture systems are briefly introduced. Furthermore, we analyze the modeling, planning, navigation, and control of the robot-assisted puncture system with both rigid and flexible needles used. Finally, the challenging issues and future trends of this field are elaborated.