The walls in our living room transitions into the ceiling with a curved surface...what is this called?
If the radius of the wall to ceiling transition is on the order of 1 to 2 inches then that corner is likely formed by use of a vinyl inside corner beading. It comes in lengths and inserted up into the corners and nailed / screwed along the edges through a flange that gets covered over with a feathered edge of drywall mud to blend the beading to the wall and ceiling surfaces. 

Sometimes a wood material is also used that looks similar to a cove moulding but that would more than likely not be used up against the drywall in a mudded in smooth transition. 

In decades gone by it was sometimes popular to create much larger radius transitions that could be a radius of 6 to 8 inches (maybe even more). These would be seen on plaster construction where curved backer corners were installed to the wall/ceiling lathe and then additional wood lathe was attached to these to create the curved surface. A professional plasterer would then plaster the wall and curved transition up to the ceiling all in one continuous process. Sorry that I cannot provide a name for that type of construction.