Computational and robotic pool has received increasing interest in the past few years. The challenges are important. In this survey, we focus on the computational aspect, but nevertheless acknowledge that the robotic aspect is both very important and very difficult. Computationally, one may roughly split the tasks into three main aspects: simulation of the physics, execution of the shots and planning of sequences of shots. We will discuss those aspects from an OR–optimization point of view. The planning aspect retains also the interest of the artificial intelligence community, and links between both approaches will be revealed. We will present the state of the art in this young research area, as well as the obstacles that remain before a computer–robotic system actually challenges a human champion.