The relevant features for a machine learning task may arrive as one or more continuous streams of data. Serving machine learning models over streams of data creates a number of interesting systems challenges in managing data routing, time-synchronization, and rate control. This paper presents EdgeServe, a distributed streaming system that can serve predictions from machine learning models in real time. We evaluate EdgeServe on three streaming prediction tasks: (1) human activity recognition, (2) autonomous driving, and (3) network intrusion detection.