The name is literal: until the early twentieth century there were fish ponds here, among them the Sasorski pond, named after its owners. When they were filled in, a market square was laid out in their place, and it has been trading ever since.
The square was once the centre of Półwsie Zwierzynieckie. Among the goods sold here was Lisiecka sausage from the villages west of Kraków, for a time traded outside official channels.
Where the square meets Michał Stachowicz Street there once stood the Bar na Stawach, distinctive enough to give its name to a collection of poems by Jerzy Harasymowicz. Stachowicz himself was a Kraków painter, whose works include a depiction of Kościuszko taking his oath on the Main Square.