Computer chess is poised to enter the final phase of its gradual march towards superiority. The best programs can now hold their own against any human being, and in most cases thrash them mercilessly. They are already substantially stronger in rapid games. Soon, computers will forge ahead and even Grandmasters won't stand a chance against them. Or will they? Are computers fundamentally limited by their lack of human intuition? Will electronic brains ever possess that certain extra element of human comprehension which has so far eluded even the most persistent research? In order to answer this question, we must investigate how computers play chess. What are the state-of-the-art algorithms that allow accurate searching of rapidly-branching game trees? I shall cover the anatomy of a chess engine from the fundamentals of board representation right up to the tree search and evaluation algorithms. I will also review the current research being carried out worldwide by groups such as the ChessBrain project and others.