A multitenant database management system (DBMS) in the cloud must continuously monitor the trade-off between efficient resource sharing among multiple application databases (tenants) and their performance. Considering the scale of hundreds to thousands of tenants in such multitenant DBMSs, manual approaches for continuous monitoring are not tenable. A self-managing controller of a multitenant DBMS faces several challenges. For instance, how to characterize a tenant given its variety of workloads, how to reduce the impact of tenant colocation, and how to detect and mitigate a performance crisis where one or more tenants' desired service level objective (SLO) is not achieved. We present Delphi, a self-managing system controller for a mul-titenant DBMS, and Pythia, a technique to learn behavior through observation and supervision using DBMS-agnostic database level performance measures. Pythia accurately learns tenant behavior even when multiple tenants share a database process, learns good and bad tenant consolidation plans (or packings), and maintains a per-tenant history to detect behavior changes. Delphi detects performance crises, and leverages Pythia to suggests remedial actions using a hill-climbing search algorithm to identify a new tenant placement strategy to mitigate violating SLOs. Our evaluation using a variety of tenant types and workloads shows that Pythia can learn a tenant's behavior with more than 92% accuracy and learn the quality of packings with more than 86% accuracy. During a performance crisis, Delphi is able to reduce 99th percentile latencies by 80%, and can consolidate 45% more tenants than a greedy baseline, which balances tenant load without modeling tenant behavior.