Transient electronic systems represent an emerging class of technology defined by an ability to physically dissolve, sublime, chemically degrade, disintegrate, or transform in a controlled manner, either spontaneously or through a trigger event. Bioresorbable (or, equivalently, bioabsorbable) electronic devices, as a subset of transient technologies, are designed to undergo complete dissolution when immersed in biofluids. Applications include temporary implants and other medical devices that serve important purposes in diagnostics and therapies, but with finite lifetimes matched to those of natural biological processes such as wound healing. Here, transience by bioresorption eliminates the devices without a trace, thereby bypassing the costs, complications, and risks associated with secondary surgical procedures for device retrieval. Such systems demand complete sets of bioresorbable electronic materials, including semiconductors, dielectrics, and conductors, as the fundamental building blocks for functional components. The considerations are not only in electronic performance, but in degradation chemistry and biocompatibility of both the materials and the products of their reactions with biofluids. This article highlights recent progress in this area of materials science and describes some of the most sophisticated bioresorbable electronic systems that combine these materials with bioresorbable polymers, the biomedical applications of these devices, and some directions for future work.