Implantable electronics address therapeutical needs of patients with electrical signaling dysfunctions such as heart problems, neurological disorders or hearing impairments. While standard electronics are rigid, planar and made of hard materials, their surrounding biological tissues are soft, wet and constantly in motion. These intrinsic differences in mechanical and chemical properties cause physiological responses that constitute a fundamental challenge to create functional long-term interfaces. Using soft and stretchable materials for electronic implants decreases the mechanical mismatch between implant and biological tissues. As a result, tissue damage during and after implantation is reduced, leading not only to an attenuated foreign body response, but also enabling completely novel applications. However, but for a few exceptions, soft materials are not sufficient to create long-term stable functional implants. In this work, we review recent progress in interfacing both the central (CNS) and peripheral nervous system (PNS) for long-term functional devices. The basics of soft and stretchable devices are introduced by highlighting the importance of minimizing physical as well as mechanical mismatch between tissue and implant in the CNS and emphasizing the relevance of an appropriate surface chemistry for implants in the PNS. Finally, we report on the latest materials and techniques that provide further electronic enhancements while reducing the foreign body reaction. Thus, this review should serve as a guide for creating long-term functional implants to enable future healthcare technologies and as a discussion on current ideas and progress within the field.