Stick-slip vibration presents one of the main problems in the quality of drilling performance limiting tool life and productivity. This type of vibration can be suppressed by means of many approaches, such as varying parameters and use of control tools. Although tremendous improvements have been made in overcoming this dysfunction, stick-slip vibration suppression remains a large problem in the drilling industry. This paper provides an up-to-date review of stick-slip vibration behavior in drillstrings. First, the phenomena and the modeling methods of stick-slip vibrations are reviewed. Then an overview of the approaches for stick-slip suppression in oilwell drillstrings is presented, grouping the references under the categories of passive vibration control and active vibration control. Literature related to passive control is grouped under the categories of optimization of bottom hole assembly (BHA) configurations, bit selection and bit redesign, and use of downhole tools. The contributions related to the active control approaches for stick-slip mitigation are grouped under the categories of drilling parameters optimization based on real-time measurement and use of active control systems. Finally, related discussions and recommendations are conducted.