The Square surrounds the market green, which has been the central point of Greenlaw since at least the late seventeenth century, when it became county town.

During the eighteenth and nineteenth centuries, two fairs were held here annually, in May and October. Also situated in The Square were a weighing machine (tron), a well and a pillory.

The Town Hall, one of the few buildings on the central green, was once also the County Court and the Castle Inn opposite would have provided accommodation for lawyers and judges.