Complexity science has always been ambivalent about the possibility to foretell the future. On one side, one of its leitmotivs has aimed at highlighting the intrinsic uncertainty and unpredictability of 'multi-scale,' 'non-linear' and 'evolutionary' systems, because of their sensitivity to initial conditions. On the other side, some complex systems specialists tackle the future almost daily but show different attitudes toward it. For example, some scholars find easier to foretell the long run evolution of a system, but only in a coarse-grained manner, while others propose to follow and predict the agents of a modeled system almost individually, thanks to their finegrained computer simulations. In this article, five anticipation communities within complexity science are described by studying their research, their normative views, their extra-academic activities, and their anticipation activity. To expound these groups in a coherent fashion, I will use and readapt for my study the concept of 'anticipation communities' introduced by French sociologist Céline Granjou. The five groups described here are named as follows: the 'high-frequency prediction,' the 'open-ended evolution,' the 'decentralized prediction,' the 'future coconstruction,' and the 'centralized anticipation' communities.