Komi Go is Go with komi. Komi was introduced in professional tournaments in the first half of the 20th century, ending the "era of no-komi go", changing the popularity of certain joseki and fuseki. The term is used when describing these differences.
Charles Matthews We've become used to komi. To put it another way, pros have been adapting their play to komi since I was born. My feeling though is that the adaptation to Komi Go was somewhat painful or empirical.
They do say that Takagawa was the first pro to adapt successfully to komi go (with komi at 4.5) in the 1950s - as demonstrated by his nine-year reign as Honinbo. Amateurs are foolish to think they can understand the content of top pro go; but in this case by all reports he was good at handling close games. Certainly the feeling of early komi go from that time is that White has little or nothing to do to catch up. Black increasingly played tight, territorial go.
In fact if you look at fuseki styles at the time (say around 1955) it's a slightly odd picture. Go Seigen and Sakata were experimenting with 3-3 openings, which had not really been systematically used in the 1930s shinfuseki period. They were also bringing back the knight's move (kogeima) enclosure, where for a long time the one-point (ikken) enclosure had reigned, for enclosing with a 3-4 point. Those are both moves in the direction of very tight, territorial play, which came even more to the fore in the Sakata period (1960-1965).
I used to think that it was Takagawa himself who persisted at this time in using 4-4 openings (nirensei, sanrensei). In fact it isn't that simple, and one can point to other players such as Miyashita and Shimamura who also consistently used 4-4 points.
Moving on into the 1960s you can see a period and a style which looks fairly classical, perhaps. The joseki tend to be the ones in the books. That however is an effect partly created by the books being compiled in that period. This looks like the mature style for go with komi=4.5 . I do feel that's misleading, to some extent. That is, if you treat go in the period 1st Meijin League (1961/2) to the advent of Rin Kaiho as Meijin about five years later as orthodox, you get a biased view. Later developments are very important - when Go Seigen talks about the importance of not being bound by corner and joseki, I think this could be illustrated by material from this time (just after he dropped down from the top level, whether or not that is significant).
After 1970 komi=5.5 became general, a fresh generation of young players came through in Japan, the Chinese style in the opening became all the rage (and sanrensei was revived), and the default opening play moved to 4-4 rather than 3-4. All these things renovated komi go. I think from that point on it became more clearly an 'arms race': Black introduced more dynamic strategies, White had to learn to cope. The current position in which many people believe komi=8 might be correct is a direct result of that process carried out over a generation, and spreading to Chinese and Korean pros.