Parallel Delta robots have the advantages of precise positioning, high stiffness, good operability, compact structure, etc., and are widely used in aviation, aerospace, subsea operations, micro-electromechanical systems, and auxiliary medical care due to these advantages. Since the development of parallel Delta robots, solving the problems of high-speed and high-precision trajectory tracking to accomplish pick-and-place tasks and other operations in large-scale or small-batch flexible manufacturing on intelligent automatic production lines has become the focus and difficulty of this field. The research and development of trajectory planning of Delta parallel robots at home and abroad are reviewed, and the current research status of trajectory planning for pick-and-place operations of Delta parallel robots is emphasized. Prospects for the development trend of parallel Delta robots are proposed, so as to provide reference for related researchers in the field of parallel Delta robot trajectory planning.