Data centers in public, private, and hybrid cloud settingsmake it possible to provision virtualmachines (VMs) with unprecedented flexibility. However, purchasing, operating, and maintaining the underlying physical resources incurs significant monetary costs and environmental impact. Therefore, cloud providers must optimize the use of physical resources by a careful allocation of VMs to hosts, continuously balancing between the conflicting requirements on performance and operational costs. In recent years, several algorithms have been proposed for this important optimization problem. Unfortunately, the proposed approaches are hardly comparable because of subtle differences in the used problem models. This article surveys the used problem formulations and optimization algorithms, highlighting their strengths and limitations, and pointing out areas that need further research. Categories and Subject Descriptors: D.4.7 [Operating Systems]: Organization and Design—Distributed systems