Axonal transport is a highly complex process essential for sustaining proper neuronal functioning. Disturbances can result in an altered neuronal homeostasis, aggregation of cargoes, and ultimately a dying-back degeneration of neurons. The impact of dysfunction in axonal transport is shown by genetic defects in key proteins causing a broad spectrum of neurodegenerative diseases, including inherited peripheral neuropathies. In this review, we provide an overview of the cytoskeletal components, molecular motors and adaptor proteins involved in axonal transport mechanisms and their implication in neuronal functioning. In addition, we discuss the involvement of axonal transport dysfunction in neurodegenerative diseases with a particular focus on inherited peripheral neuropathies. Lastly, we address some recent scientific advances most notably in therapeutic strategies employed in the area of axonal transport, patient-derived iPSC models, in vivo animal models, antisense-oligonucleotide treatments, and novel chemical compounds.