Branched nanostructures represent unique, 3D building blocks for the “bottom-up” paradigm of nanoscale science and technology. Here, we report a rational, multistep approach toward the general synthesis of 3D branched nanowire (NW) heterostructures. Single-crystalline semiconductor, including groups IV, III–V, and II–VI, and metal branches have been selectively grown on core or core/shell NW backbones, with the composition, morphology, and doping of core (core/shell) NWs and branch NWs well controlled during synthesis. Measurements made on the different composition branched NW structures demonstrate encoding of functional p-type/n-type diodes and light-emitting diodes (LEDs) as well as field effect transistors with device function localized at the branch/backbone NW junctions. In addition, multibranch/backbone NW structures were synthesized and used to demonstrate capability to create addressable nanoscale LED arrays, logic circuits, and biological sensors. Our work demonstrates a previously undescribed level of structural and functional complexity in NW materials, and more generally, highlights the potential of bottom-up synthesis to yield increasingly complex functional systems in the future.