Several efforts have been carried out to enhance dexterous hand prosthesis control by impaired individuals. Choosing which voluntary signal to use for control purposes is a critical element to achieve this goal. This review presents and discusses the recent results achieved by using electromyographic signals, recorded either with surface (sEMG) or intramuscular (iEMG) electrodes, and electroneurographic (ENG) signals. The potential benefits and shortcomings of the different approaches are described with a particular attention to the definition of all the steps required to achieve an effective hand prosthesis control in the different cases. Finally, a possible roadmap in the field is also presented.