Our goal with this research manifesto is to define a roadmap to guide the evolution of the new research field that is emerging at the intersection between crowdsourcing and the Semantic Web. We analyze the confluence of these two disciplines by exploring their relationship. First, we focus on how the application of crowdsourcing techniques can enhance the machine-driven execution of Semantic Web tasks. Second, we look at the ways in which machine-processable semantics can benefit the design and management of crowdsourcing projects. As a result, we are able to describe a list of successful or promising scenarios for both perspectives, identify scientific and technological challenges, and compile a set of recommendations to realize these scenarios effectively. This research manifesto is an outcome of the Dagstuhl Seminar 14282: Crowdsourcing and the Semantic Web.