What do we know about the Last Universal Common Ancestor (LUCA)?
Carl Woese has much to say on this subject, including:


  “The ancestor cannot have been a particular organism, a single
  organismal lineage. It was communal, a loosely knit, diverse
  conglomeration of primitive cells that evolved as a unit, and it
  eventually developed to a stage where it broke into several distinct
  communities, which in their turn become the three primary lines of
  descent [bacteria, archaea and eukaryotes].”


There is a 2000 Scientific American article by W.F. Doolittle that discusses much of Woese's (and others') work understanding this question.

Also, see a couple of Woese articles here and here.