Systems and methods are described implementing streaming analytics on a serverless compute system. A user can specify a data stream against which analytics should be conducted, serverless functions to be used to conduct the analysis, and criteria for the analytics, such as windowing criteria and aggregation criteria. The windowing criteria can specify windows of items within the stream that should be collectively analyzed. The aggregation criteria can specify how to group items within each window during analysis. A poller device can read data items from the stream, window and group the items according to the windowing and aggregation criteria, and invoke serverless functions to conduct streaming analytics on the data items. The poller device can further maintain state between invocations.