Stream processing has recently gained a prominent role in Computer Science research. From networks or databases to information theory or programming languages, a lot of work has been dedicated to conceive ways of representing, transmitting, processing and understanding infinite sequences of data. Nevertheless, there are still aspects that need time to reach a mature state. In particular, heterogeneity in stream data management and event processing is both a challenging topic and a key enabler for the rising Web of Things, where smart devices continuously sense properties of the surrounding world. Different proposals on RDF and Linked Data streams have shown promising results for managing this type of data, while keeping explicit semantics on the data streams, and linking them to other datasets in a web-friendly way. With time, these efforts led to the emergence of initiatives such as the RDF Stream Processing (RSP) W3C community group, aiming at specifying a base RDF stream model and query language for that model. Although these works produced interest results in defining overarching model definitions, there are still multiple orthogonal challenges that need to be addressed. In this work we identify some of these challenges, and we link them to the characteristics of what are nowadays called reactive systems. This paradigm includes natively supporting event-driven asynchronous message passing, non-blocking data communication and processing through all layers, and on-demand flexible scalability. We argue that RDF stream systems, combined with reactive techniques can lead to powerful, resilient and interoperable systems at Web scale.