Recent advances in sensing technology have enabled a new generation of tabletop displays that can sense multiple points of input from several users simultaneously. However, apart from a few demonstration techniques [17], current user interfaces do not take advantage of this increased input bandwidth. We present a variety of multifinger and whole hand gestural interaction techniques for these displays that leverage and extend the types of actions that people perform when interacting on real physical tabletops. Apart from gestural input techniques, we also explore interaction and visualization techniques for supporting shared spaces, awareness, and privacy. These techniques are demonstrated within a prototype room furniture layout application, called RoomPlanner.