Neurointerfaces have acquired major relevance as both rehabilitative and therapeutic tools for patients with spinal cord injury, limb amputations and other neural disorders. Bidirectional neural interfaces are a key component for the functional control of neuroprosthetic devices. The two main neuroprosthetic applications of interfaces with the peripheral nervous system (PNS) are: the refined control of artificial prostheses with sensory neural feedback, and functional electrical stimulation (FES) systems attempting to generate motor or visceral responses in paralyzed organs. The results obtained in experimental and clinical studies with both, extraneural and intraneural electrodes are very promising in terms of the achieved functionality for the neural stimulation mode. However, the results of neural recordings with peripheral nerve interfaces are more limited. In this paper we review the different existing approaches for PNS signals recording, denoising, processing and classification, enabling their use for bidirectional interfaces. PNS recordings can provide three types of signals: i) population activity signals recorded by using extraneural electrodes placed on the outer surface of the nerve, which carry information about cumulative nerve activity; ii) spike activity signals recorded with intraneural electrodes placed inside the nerve, which carry information about the electrical activity of a set of individual nerve fibers; and iii) hybrid signals, which contain both spiking and cumulative signals. Finally, we also point out some of the main limitations, which are hampering clinical translation of neural decoding, and indicate possible solutions for improvement.