Connes has on his home page a very nice downloadable survey article "A view of mathematics" which also gives a good idea of the role of groupoids in this area, and links with many topics mentioned by others above. 

I have also raised the question of the problem of applying these or related techniques to algebraically structured groupoids: 

https://mathoverflow.net/questions/86617/convolution-algebras-for-double-groupoids 

Since "motivating graduate students" was part of the original question, someone needs to point out at least one thing that has not been done.  It can be useful to explain the "exterior" of a subject: unknowns, known unknowns, etc! One would also like the experts to point out anomalies in this area: I won't try to define this term, but they can lie around unrecognised.