Internet data centers are developing towards a diversified, intelligent, automated, large-scaled, and standardized direction. With the increasing of scale and complexity, it brings great challenges in how to effectively manage resources. Currently, resource management has become a major issue in Internet data centers, and its importance and urgency cannot be ignored. This paper analyzes two major challenges of resource management with which the Internet data center is facing: (1) meeting the compatibility of concurrent and multiple application SLAs (service level agreements); (2) improving the energy efficiency of system service. Based on the challenges, this paper thoroughly analyzes and summarizes the related work of resource management guaranteeing the SLA, reducing power, and incorporating the objectives of guaranteeing the SLA and reducing power simultaneously during the last ten years. Finally, the paper summaraizes the research and points out future research directions.