There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer.

I thought it would be great to have all the information in one place.
A couple of questions to start:

1. How to specify multiple levels, where one group is nested within the other. is it (1|group1:group2) or (1+group1|group2)
2. What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc. 
3. How to specify group level interactions

Basically any thoughts are welcome.