Last month the computer Go program AlphaGo beat a top human player, Lee Sedol, 4-1 in a 5 game match. Long ago I studied Go some but never played enough to become very good. However I know the basics and was able to follow the match with some interest (despite the live games being at an inconvenient time). Go is a harder game for computers to play than chess and 20 years ago when IBM's computer chess program, Deep Blue, was playing Garry Kasparov, computer Go programs were pretty bad. So there has been a lot of progress. I see three big contributors to this milestone. First a new algorithm, Monte Carlo tree search (MCTS), developed about 10 years ago, proved to work very well for Go. Second there has been continuous progress in machine learning, in particular deep learning for artificial neural networks. Third computer technology continues to advance rapidly. Modern graphics processing units (GPUs) provide incredible computational power for suitable problems and this has contributed to recent advances in deep learning.
If you are interested in playing an online computer Go program check out the Cosumi site. It provides a variety of skill levels and board sizes (standard Go is played on a 19x19 grid but smaller sizes make for a faster game and are easier for computers to handle). I have played some 9x9 games against it. I find it an entertaining opponent. At level 5 (the highest level provided) it still moves quickly but can beat me most of the time despite the occasional weird blunder. I recommend the 2-click setting to avoid frustrating unintended moves. Unfortunately the FAQ is in Japanese so I don't know anything about the underlying program. Apparently it has been around for a while but I didn't discover it until the match got me interested in Go again.