ARU and LYC are the main ones. Have a look at their website to get some background on this market (they used have some some interesting reports, some of the scoping studies had a lot of industry information). It is a very small market, with China the dominant producer. The USA is re-opening its old mine (Mountain Pass). There are environmental issues associated with the processing of the ore.
There are some explorers (eg NAV and ALK) both of which are into gold as well. Is GGG another one, which also has uranium? The general thread has some posts today about REE explorers and an interesting article in the Australian (13 September by Robin Bromby who has written a few other articles on this industry).