We present a recently invented approach to combine broad classes of dissimilar materials into heterogeneously integrated (HGI) electronic systems with two or three dimensional (3D) layouts. We have developed a process, called transfer printing, to transfer high performance semiconductor materials such as silicon, gallium arsenide, gallium nitride, indium phosphide onto rigid or flexible substrates. One of the objectives of this approach is to enable the fine-scale integration of compound semiconductors (CS) with standard silicon-based integrated circuit technologies, eg. CMOS, to develop high performance HGI electronics systems on rigid or flexible substrates.