Methods and apparatus for additive manufacturing of three-dimensional objects from polymerizable liquids are described. The methods and apparatus are implemented in the form of a bottom up additive manufacturing apparatus, and in preferred embodiments are implemented in the form of Continuous Liquid Interface Production (or “CLIP”) methods and apparatus. Rotation of at least one of the carrier and the build plate is preferably included, for example to facilitate the filling of the build region with the polymerizable liquid.