The loss of a hand can significantly affect one’s work and social life. For many patients, an artificial limb can improve their mobility and ability to manage everyday activities, as well as provide the means to remain independent. This paper provides an extensive review of available biosensing methods to implement the control system for transradial prostheses based on the measured activity in remnant muscles. Covered techniques include electromyography, magnetomyography, electrical impedance tomography, capacitance sensing, near-infrared spectroscopy, sonomyography, optical myography, force myography, phonomyography, myokinetic control, and modern approaches to cineplasty. The paper also covers combinations of these approaches, which, in many cases, achieve better accuracy while mitigating the weaknesses of individual methods. The work is focused on the practical applicability of the approaches, and analyses present challenges associated with each technique along with their relationship with proprioceptive feedback, which is an important factor for intuitive control over the prosthetic device, especially for high dexterity prosthetic hands.