Peripheral nerve interfaces (PNIs) record and/or modulate neural activity of nerves, which are responsible for conducting sensory-motor information to and from the central nervous system, and for regulating the activity of inner organs. PNIs are used both in neuroscience research and in therapeutical applications such as precise closed-loop control of neuroprosthetic limbs, treatment of neuropathic pain and restoration of vital functions (e.g. breathing and bladder management). Implantable interfaces represent an attractive solution to directly access peripheral nerves and provide enhanced selectivity both in recording and in stimulation, compared to their non-invasive counterparts. Nevertheless, the long-term functionality of implantable PNIs is limited by tissue damage, which occurs at the implant-tissue interface, and is thus highly dependent on material properties, biocompatibility and implant design. Current research focuses on the development of mechanically compliant PNIs, which adapt to the anatomy and dynamic movements of nerves in the body thereby limiting foreign body response. In this paper, we review recent progress in the development of flexible and implantable PNIs, highlighting promising solutions related to materials selection and their associated fabrication methods, and integrated functions. We report on the variety of available interface designs (intraneural, extraneural and regenerative) and different modulation techniques (electrical, optical, chemical) emphasizing the main challenges associated with integrating such systems on compliant substrates.