Combinatorial game solving is a research field that is frequently highlighted each time a program defeats the best human player: Deep Blue (IBM) vs Kasparov for Chess in 1997, and Alpha Go (Google) vs Lee Sedol for the game of Go in 2016. But what is hidden behind these success stories ? First of all, I will consider combinatorial games from a theoretical point of view. We will see how to proceed to properly define and deal with the concepts of outcome, value, and winning strategy. Are there some games for which an exact winning strategy can be expected? Unfortunately, the answer is no in many cases (including some of the most famous ones like Go, Othello, Chess or Checkers), as exact game solving belongs to the problems of highest complexity. Therefore, finding out an effective approximate strategy has highly motivated the community of AI researchers. In the current survey, the basics of the best AI programs will be presented, and in particular the well-known Minimax and Monte-Carlo Tree Search approaches.