About 20 years ago, Guoliang Yu proved a spectacular theorem relating the coarse Baum-Connes conjecture to coarse embeddability into Hilbert space. Our understanding of the coarse geometry of unbounded metric spaces has by now reached a somehow satisfactory stage but many important questions remain open. In this talk, we will browse some important results and techniques that have appeared in the span between Yu's breakthrough result and a recent result of the speaker, G. Lancien and Th. Schlumprecht asserting that Hilbert space is not coarsely minimal.