The rapid growth of virtualized data centers and cloud hosting services is making the management of physical resources such as CPU, memory, and I/O bandwidth in data center servers increasingly important. Server management now involves dealing with multiple dissimilar applications with varying Service-Level-Agreements (SLAs) and multiple resource dimensions. The multiplicity and diversity of resources and applications are rendering administrative tasks more complex and challenging. This thesis aimed to develop a framework and techniques that would help substantially reduce data center management complexity. We specifically addressed two crucial data center operations. First, we precisely estimated capacity requirements of client virtual machines (VMs) while renting server space in cloud environment. Second, we proposed a systematic process to efficiently allocate physical resources to hosted VMs in a data center. To realize these dual objectives, accurately capturing the effects of resource allocations on application performance is vital. The benefits of accurate application performance modeling are multifold. Cloud users can size their VMs appropriately and pay only for the resources that they need; service providers can also offer a new charging model based on the VMs performance instead of their configured sizes. As a result, clients will pay exactly for the performance they are actually experiencing; on the other hand, administrators will be able to maximize their total revenue by utilizing application performance models and SLAs. This thesis made the following contributions. First, we identified resource control parameters crucial for distributing physical resources and characterizing contention for virtualized applications in a shared hosting environment. Second, we explored several modeling techniques and confirmed the suitability of two machine learning tools, Artificial Neural Network and Support Vector Machine, to accurately model the performance of virtualized applications. Moreover, we suggested and evaluated modeling optimizations necessary to improve prediction accuracy when using these modeling tools. Third, we presented an approach to optimal VM sizing by employing the performance models we created. Finally, we proposed a revenue-driven resource allocation algorithm which maximizes the SLA-generated revenue for a data center.