Bidirectional interfacing between electrode and biological system has enabled diagnostics and therapeutics in modern medicine, however the inherent dissimilarity between the soft, ion-rich, dynamic biological tissues and the rigid, dry, static electronic systems hinders the establishment of effective and reliable bioelectronic interfaces. In the past decade, the scope of flexible/stretchable electronics has been broadened into bioelectronics owing to the need of implementation of various biocompatible soft conductors. This review discusses the basic requirements for the construction of both epidermal and implantable bioelectronic interfaces utilizing soft materials, and summarizes the most recent progress in the development of soft conductors which are customized to interface with skin and other tissues. The conclusion provides an outlook on the remaining obstacles and outlines possible strategies to facilitate the technological advances in bioelectronics.