Following the experimental discovery of topological insulators, intensive work over the last five years has revealed that these are just the tip of the iceberg of a wider set of topological phenomena that occur in solids. I will discuss recent breakthroughs in this rapidly advancing field. First I will talk about Weyl semimetals, which provide a realization of Weyl’s 85 year old equation and which possess an exotic Fermi surface that spans opposite faces of a sample. Next, I will talk about another class of topological phases – quantum spin liquids –and progress in identifying experimental candidates. Finally, I will discuss the important role quantum entanglement has played in these developments.