I'll describe a cofibrantly-generated Quillen model structure on the category 2-Cat of 2-categories and 2-functors; the weak equivalences are the biequivalences, and 2-functors are (right) homotopic if and only if they are pseudonaturally equivalent. The model structure is proper, in the sense that weak equivalences are stable under pullback along fibrations and pushout along cofibrations. It is compatible with the monoidal structure given by the Gray tensor product, but not with the cartesian monoidal structure.
[This has been written up as a paper of the same name, published in K-theory 26(2002), 171-205. It contains an error, which is corrected in A Quillen model structure for bicategories.]