The abilities of the human hand have always fascinated people, and many studies have been devoted to describing and understanding a mechanism so perfect and important for human activities. Hand loss can significantly affect the level of autonomy and the capability of performing the activities of daily life. Although the technological improvements have led to the development of mechanically advanced commercial prostheses, the control strategies are rather simple (proportional or on/off control). The use of these commercial systems is unnatural and not intuitive, and therefore frequently abandoned by amputees. The components of an active prosthetic hand are the mechatronic device, the decoding system of human biological signals into gestures and the control law that translates all the inputs into desired movements. The real challenge is the development of a control law replacing human hand functions. This paper presents a literature review of the control strategies of prosthetics hands with a multiple-layer or hierarchical structure, and points out the main critical aspects of the current solutions, in terms of human's functions replicated with the prosthetic device. The paper finally provides several suggestions for designing a control strategy able to mimic the functions of the human hand.