Compared to chess, Go has been a far more difficult game for computer engines to master. The larger search space (up to 381 possible moves per ply to search) has meant that brute force techniques haven't been that useful. At first this problem lead to researcher only looking a smaller boards (9x9) but then a modified Monte Carlo method provided the next leap in strength.
Now researches at Google have developed a program strong enough to beat the European Go champion. Using neural nets the researchers were able to train the program to recognise positions and moves that were likely to lead to a favourable position, and from there the program's strength grew. As mentioned in this report, at first the program was very week, but after examining 30 million moves, and playing against itself, it twigged to what was needed to be a strong player. Having conquered Go in Europe, the big challenge would be for the program to take on the best players in Asia. I am not sure whether this will happen (although I do not think Man v Machine matches in Go are banned, as they are in Shogi) as the researchers are talking about moving their research in other directions.