Note on the Hopfield model
To simplify is the greatest form of sophistication. -Leonardo da Vinci
I wrote a brief review on some basic properties of the Hopfield model. It is available here. I really like the Hopfield model, because I think one should always work with the simplest model one can get away with and the Hopfield model is certainly one of the simplest models one can use to study collective phenomena in neural networks. Of course, one cannot explain everything in terms of Hopfield-type models, but surprisingly, in a lot of cases, the level of abstraction provided by the Hopfield turns out to be sufficient to qualitatively explain interesting phenomena. For example, here is a nice paper that explains, among other things, why spontaneous activity in the cortex should have the same structure as stimulus-evoked activity as has been observed experimentally, using a very simple Hopfield-type model.
Also, there is a large and rich body of theoretical results on the Hopfield model and its variants, thanks in large measure to the efforts of physicists. So, people who want to study an interesting collective behavior in neural networks can quickly build on an already existing literature.