Modern datacenter servers hosting popular Internet services face significant and multi-facet challenges in performance and power control. The user-perceived performance is the result of a complex interaction of complex workloads in a very complex underlying system. Highly dynamic and bursty workloads of Internet services fluctuate over multiple time scales, which has a significant impact on processing and power demands of datacenter servers. High-density servers apply virtualization technology for capacity planning and system manageability. Such virtualized computer systems are increasingly large and complex. This paper surveys representative approaches to autonomic performance and power control on virtualized servers, which control the quality of service provided by virtualized resources, improve the energy efficiency of the underlying system, and reduce the burden of complex system management from human operators. It then presents three designed self-adaptive resource management techniques based on machine learning and control for percentile-based response time assurance, non-intrusive energy-efficient performance isolation, and joint performance and power guarantee on virtualized servers. The techniques were implemented and evaluated in a testbed of virtualized servers hosting benchmark applications. Finally, two research trends are identified and discussed for sustainable cloud computing in green datacenters. Modern datacenter servers hosting popular Internet services face significant and multi-facet challenges in performance and power control. The user-perceived performance is the result of a complex interaction of complex workloads in a very complex underlying system. Highly dynamic and bursty workloads of Internet services fluctuate over multiple time scales, which has a significant impact on processing and power demands of datacenter servers. High-density servers apply virtualization technology for capacity planning and system manageability. Such virtualized computer systems are increasingly large and complex. This paper surveys representative approaches to autonomic performance and power control on virtualized servers, which control the quality of service provided by virtualized resources, improve the energy efficiency of the underlying system, and reduce the burden of complex system management from human operators. It then presents three designed self-adaptive resources management tech niques based on machine learning and control for percentile-based response time assurance, non-intrusive energy-efficient performance isolation, and joint performance and power guarantee on virtualized servers. The techniques were implemented and evaluated in a testbed of virtualized servers hosting benchmark applications. Finally, two research trends are identified and discussed for sustainable cloud computing in green datacenters.