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Computer Go is a game that has been used for many years as a challenge for AI. AlphaGo has received significant press coverage lately, after achieving a victory that surprised many experts in the field. But progress and work within the Go community, pushing the boundaries of research in this game, has been steady over the years before this breakthrough. In this talk, we will review the progress and paradigm shifts from the early days of computer Go to the recent victory of AlphaGo using Deep Learning and Monte Carlo Tree Search, and we will outline possible future directions on this field.