Cloud computing promises flexibility and high performance for users and high cost-efficiency for operators. Nevertheless, most cloud facilities operate at very low utilization, hurting both cost effectiveness and future scalability. We present Quasar, a cluster management system that increases resource utilization while providing consistently high application performance. Quasar employs three techniques. First, it does not rely on resource reservations, which lead to underutilization as users do not necessarily understand workload dynamics and physical resource requirements of complex codebases. Instead, users express performance constraints for each workload, letting Quasar determine the right amount of resources to meet these constraints at any point. Second, Quasar uses classification techniques to quickly and accurately determine the impact of the amount of resources (scale-out and scale-up), type of resources, and interference on performance for each workload and dataset. Third, it uses the classification results to jointly perform resource allocation and assignment, quickly exploring the large space of options for an efficient way to pack workloads on available resources. Quasar monitors workload performance and adjusts resource allocation and assignment when needed. We evaluate Quasar over a wide range of workload scenarios, including combinations of distributed analytics frameworks and low-latency, stateful services, both on a local cluster and a cluster of dedicated EC2 servers. At steady state, Quasar improves resource utilization by 47% in the 200-server EC2 cluster, while meeting performance constraints for workloads of all types.