I've been reading a lot of Greek, Roman and Norse history recently and began to wonder why they had so many rowers. What made them obsolete and why?
Oar-driven warships remained widely in service far after the Greeks, Romans, or Norse. They were used well into the 16th century until what is aptly called the Age of Sail, when sailing ships became the standard. Technology and the expanded demand for long-range capability drove this change.
Rowers were not generally meant as a primary method of propulsion, but to augment or work in tandem with sails. A ship with rowers had the advantage that it could move independent of the wind, and with superior mobility compared to the sails of the day, particularly in close battle. However, oared ships also had disadvantages in that they had to be very low to accommodate rowing, and required a lot of manpower and supplies to be able to row and fight. This made oared ships best-suited for short-range operations in easy waters - they couldn't hold enough supplies to go very far, nor were they suited for the rough open seas.
Eventually, technological improvements, primarily in sailing and cannon, tipped the balance heavily against oars. Improved sailing ships became much faster than oared ships, with much improved control and handling due to better hulls and sailing technique. Cannon extended the range and nature of combat, negating the oars' advantage at short-range ram-and-board tactics. While sail ships could design hulls to take advantage of these new technologies and methods, oared ships could not because of the need to accommodate rowing.
Because they had smaller crews and superior hulls, sail ships also had much greater range and cargo space. In the ages of exploration and colonialism, the ability to exploit the open ocean also proved an insurmountable advantage for sail. Powers that could or would not adopt surrendered this advantage to others. This combination of tactical inefficiency and limited range rendered oared ships obsolete in terms of naval power.