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We developed a simple approach to combine broad classes of dissimilar materials into heterogeneously integrated electronic systems with two- or three-dimensional layouts. The process begins with the synthesis of different semiconductor nanomaterials, such as single-walled carbon nanotubes and single-crystal micro- and nanoscale wires and ribbons of gallium nitride, silicon, and gallium arsenide on separate substrates. Repeated application of an additive, transfer printing process that uses soft stamps with these substrates as donors, followed by device and interconnect formation, yields high-performance heterogeneously integrated electronics that incorporate any combination of semiconductor nanomaterials on rigid or flexible device substrates. This versatile methodology can produce a wide range of unusual electronic systems that would be impossible to achieve with other techniques.