In this presentation we will discuss our recent progress on the integration of InAs/Si p-tunnel FETs (TFETs) and InAs/GaSb n-TFETs on SOI wafers. Local III-V growth is enabled by the development of Template-Assisted Selective Epitaxy (TASE) [1-4]. Both polarity devices have scaled geometries with cross-sections on the order of 30nm. The p-channel InAs/Si TFETs are developed based on our previously demonstrated vertical devices, which are now implemented horizontally in-plane on the Si wafer. The InAs/Si TFETs show excellent performance with Ion of about 4μA/μm at Vgs = Vds = -0.5V, combined with average subthreshold swings (SS) of 70-80mV/dec. The SS is limited by trap mechanisms at the heterojunction, which will also be discussed. The InAs/GaSb n-TFETs represent our first devices in this material system, with doping levels and gate stack not yet optimized; the all III-V TFETs show about an order of magnitude greater current levels, but at a worse SS.