The increasing deployment of multiple unmanned vehicles systems has generated large research interest in recent decades. This paper therefore provides a detailed survey to review a range of techniques related to the operation of multi-vehicle systems in different environmental domains, including land based, aerospace and marine with the specific focuses placed on formation control and cooperative motion planning. Differing from other related papers, this paper pays a special attention to the collision avoidance problem and specifically discusses and reviews those methods that adopt flexible formation shape to achieve collision avoidance for multi-vehicle systems. In the conclusions, some open research areas with suggested technologies have been proposed to facilitate the future research development.