Embodiments in accordance with the present disclosure are directed to non-invasive or essentially non-invasive electrode structures, assemblies, and devices for sensing neural signals carried or produced by peripheral nerves, and/or applying stimulation signals to peripheral nerves. Electrode structures, assemblies, and devices in accordance with embodiments of the present disclosure include (a) flexible epineural strip electrode structures having one or more elongate electrode-carrying strips that can be adhered (e.g., glued) and/or sutured to a peripheral nerve; (b) flexible elongate ribbon electrode structures, which can be spirally wound about portions of a peripheral nerve's length such that microneedle and/or disc or stud type electrodes carried by the ribbon electrode structure are disposed in a helical arrangement about the peripheral nerve; and (c) an embedded nerve tissue—electrode interface having a tubular compartment containing adipose tissue that supports axonal tissue ingrowth and interfacing of ingrown axonal tissue with electrode microwires in the compartment.