A new generation of Web Applications is pushing the Web infrastructure to process data as soon as they arrive and before they are no longer valuable. However, the Web infrastructure as it is not adequate, and Stream Processing technologies cannot deal with heterogeneous data streams and events. To solve these issues, we need to investigate how to identify, represent, and process streams and events on the Web. In this chapter, we discuss the recent advancements for taming Velocity on the Web of Data without neglecting Data Variety. Thus, we present a Design Science research investigation that builds on the state of the art of Stream Reasoning and RDF Stream Processing. We present our research results, for representing and processing stream and events on the Web, and we discuss their potential impact.