IceTop is the surface component of the IceCube Observatory, composed of frozen water tanks at the top of IceCube’s strings. Data from this detector can be analyzed in different ways with the goal of measuring cosmic ray spectrum and composition. The shower size S125 from IceTop alone can be used as a proxy for primary energy, and unfolded into an all-particle spectrum. In addition, S125 from the surface can be combined with high-energy muon energy loss information from the deep IceCube detector for those air showers which pass through both. Using these coincident events in a complementary analysis, both the spectrum and mass composition of primary cosmic rays can be extracted in parallel using a neural network. Both of these analyses have been performed on three years of IceTop and IceCube data. Both all-particle spectra as well as individual spectra for elemental groups are presented.