A message processing technology is provided that includes subscription of stateless compute functions to messaging queues of the message queueing service. The message queueing service may be configured to provide highly scalable hosted messaging queues for reliable delivery of messages. When messages are received in a messaging queue, then a stateless compute function, of a serverless compute service, that is subscribed to the messaging queue may be invoked to process the message. The serverless compute service manages compute resource for execution of the stateless compute function in response to dynamic message traffic.