Support structures are required for most Additive Manufacturing technologies, to provide a base for overhangs (FDM), connect disjoint components to the print bed (SLA), or mitigate part warping (SLS). The strategies for automatic support structure generation widely employed by the Additive Manufacturing industry are relatively primitive, in that they do not leverage modern geometric computing techniques. As a result, support structures are one of the most frequent sources of print failure. We propose a more advanced type of support structure, in the form of a branching hierarchy of support posts. A top-down generative algorithm is used to “grow” a support structure from the regions which must be supported down to the model or build plate. This strategy results in much sparser support, often saving 75% or more of support material over standard techniques, reducing print time by 50% or more for larger prints, and also produces fewer surface artifacts. Our support generator is freely available in Autodesk Meshmixer, and is widely used in the consumer FDM/FFF space. We have recently extended our technique to handle support structures for SLA. We will also discuss improvements in the handling of large planar overhangs, and efficient techniques to optimize support structure robustness.