In view of the problems of highly redundant degree-of-freedoms, strongly dynamic coupling between manipulator(s) and mobile platform of the Ground mobile manipulators (GMM), some challenging puzzles in GMMs are still being open, including equivalent dynamics modelling of action chain and its simplification method, the high-dimensional dynamic manipulate planning under strong environmental interaction, dynamic stability, as well as real-time manipulator control, and so forth. Focusing on dynamic modelling and coupling analysis, motion planning, dynamic stability, and manipulator control of the GMMs, current literatures are investigated and a review on the state-of-the-art of whole-body motion planning and control of the GMMs is presented. Some key problems and technical challenges are summarized, and the future direction is prospected.