I will give an update on the dictionary between the representations of quantum toroidal algebras and branes of Type IIB string theory. I will argue that brane crossings correspond to R-matrices, of which the “degenerate resolved conifold” is one example. A more interesting example is given by the “Hanany-Witten R-matrix”, for which the brane creation effect and Hanany-Witten rules become algebraic identities.