Myoelectric control for prosthetic hands is an important topic in the field of rehabilitation. Intuitive and intelligent myoelectric control can help amputees to regain upper limb function. However, current research efforts are primarily focused on developing rich myoelectric classifiers and biomimetic control methods, limiting prosthetic hand manipulation to simple grasping and releasing tasks, while rarely exploring complex daily tasks. In this article, we conduct a systematic review of recent achievements in two areas, namely, intention recognition research and control strategy research. Specifically, we focus on advanced methods for motion intention types, discrete motion classification, continuous motion estimation, unidirectional control, feedback control, and shared control. In addition, based on the above review, we analyze the challenges and opportunities for research directions of functionality-augmented prosthetic hands and user burden reduction, which can help overcome the limitations of current myoelectric control research and provide development prospects for future research.