The binding of intrinsically disordered proteins (IDPs) to structured targets is gaining increasing attention. Here we review experimental and computational studies on the binding kinetics of IDPs. Experiments have yielded both the binding rate constants and the binding mechanisms, the latter via mutation and deletion studies and NMR techniques. Most computational studies have aimed at qualitative understanding of the binding rate constants or at mapping the free energy surfaces after the IDPs are engaged with their targets. The experiments and computation show that IDPs generally gain structures after they are engaged with their targets; that is, interactions with the targets facilitate the IDPs' folding. It also seems clear that the initial contact of an IDP with the target is formed by just a segment, not the entire IDP. The docking of one segment to its sub-site followed by coalescing of other segments around the corresponding sub-sites emerges as a recurring feature in the binding of IDPs. Such a dock-and-coalesce model forms the basis for quantitative calculation of binding rate constants. For both disordered and ordered proteins, strong electrostatic attraction with their targets can enhance the binding rate constants by several orders of magnitude. There are now tremendous opportunities in narrowing the gap in our understanding of IDPs relative to ordered proteins with regard to binding kinetics.