The city's oldest surviving gatehouse dates from the city walls of 1488. After the city expanded, it became the public weigh house for farmers coming into town with the produce. It's also been home to executions and various guilds. Rembrandt painted his two anatomy lesson paintings for the Guild of Surgeons which was based here.
Now the Waag houses the Society for Old and New Media which is (and I quote) "a knowledge institute operating on the cutting edge of culture and technology in relation to society, education, government and industry....The interplay of technology and culture is the driving force of all Waag Society's activities."
Well, it has a great café terrace anyway.