We present Henge, a system to support intent-based multi-tenancy in modern distributed stream processing systems. Henge supports multi-tenancy as a first-class citizen: everyone in an organization can now submit their stream processing jobs to a single, shared, consolidated cluster. Secondly, Henge allows each job to specify its own intents (i.e., requirements) as a Service Level Objective (SLO) that captures latency and/or throughput needs. In such an intent-driven multi-tenant cluster, the Henge scheduler adapts continually to meet jobs’ respective SLOs in spite of limited cluster resources, and under dynamically varying workloads. SLOs are soft and are based on utility functions. Henge’s overall goal is to maximize the total system utility achieved by all jobs in the system. Henge is integrated into Apache Storm and we present experimental results using both production jobs from Yahoo! and real datasets from Twitter.