The aim of process discovery, originating from the area of process mining, is to discover a process model based on business process execution data. A majority of process discovery techniques relies on an event log as an input. An event log is a static source of historical data capturing the execution of a business process. In this paper we focus on process discovery relying on online streams of business process execution events. Learning process models from event streams poses both challenges and opportunities, i.e. we need to handle unlimited amounts of data using finite memory and, preferably, constant time. We propose a generic architecture that allows for adopting several classes of existing process discovery techniques in context of event streams. Moreover, we provide several instantiations of the architecture, accompanied by implementations in the process mining tool-kit ProM (http://promtools.org). Using these instantiations, we evaluate several dimensions of stream-based process discovery. The evaluation shows that the proposed architecture allows us to lift process discovery to the streaming domain.