Stretchable electronics is an emerging technology that creates devices with the ability to conform to nonplanar and dynamic surfaces such as the human body. Current stretchable configurations are constrained to single-layer designs due to limited material processing capabilities in soft electronic systems. Here we report a framework for engineering three-dimensional integrated stretchable electronics by combining strategies in material design and advanced microfabrication. Our three-dimensional devices are built layer by layer through transfer printing pre-designed stretchable circuits on elastomers and creating vertical interconnect accesses using laser ablation and controlled soldering. Our approach enables a higher integration density on stretchable substrates than single-layer approaches and allows new functionalities that would be difficult to implement with conventional single-layer designs. Using this engineering framework, we create a stretchable human–machine interface testbed that is based on a four-layer design and offers eight-channel sensing and Bluetooth data communication capabilities.By combining strategies in material design and advanced microfabrication, three-dimensional integrated stretchable electronic devices can be created, including an eight-channel sensing system with Bluetooth communication capabilities that can be used to extract an array of signals from the human body.