Biodegradable electronic systems represent an emerging class of technology with unique application possibilities, from temporary biomedical implants to "green" consumer gadgets. This paper introduces materials and processing methods for 3D, heterogeneously integrated devices of this type, with various functional examples in sophisticated forms of silicon-based electronics. Specifically, techniques for performing multilayer assembly by transfer printing and for fabricating layer-to-layer vias and interconnects by lithographic procedures serve as routes to biodegradable, 3D integrated circuits composed of functional building blocks formed using specialized approaches or sourced from commercial semiconductor foundries. Demonstration examples range from logic gates and analog circuits that undergo functional transformation by transience to systems that integrate multilayer resistive sensors for in situ, continuous electrical monitoring of the processes of transience. The results significantly expand the scope of engineering options for biodegradable electronics and other types of transient microsystem technologies.