Warped cones are constructions introduced by John Roe from discrete group actions on compact spaces to obtain examples of coarse spaces which do not have property A or which are not coarsely embeddable into Hilbert space. These spaces have recently attracted a great deal of interest. In particular, super expander graphs are constructed from certain warped cones. In this talk, we will first review some of recent development on the coarse geometry of warped cones and expanders, and then discuss the coarse Novikovconjecture of warped cones which admit a fibred coarse embedding into a Banach space with property (H).

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