The game is set as a clash between neighboring dynasties at the dawn of civilization. The game is named after the rivers Tigris and Euphrates in the region now called the Middle-East. The rivers together formed natural borders for an area which harboured several grand ancient civilizations, including Sumer, Babylonia, and Assyria. The Greeks called this area Mesopotamia, which literally means "between the rivers".
The board is a map of the two rivers, marked with a square grid. There are four types of tiles with corresponding leaders: temples and priests (red), farms and farmers (blue), markets and merchants (green) and settlements and kings (black). The game starts with ten isolated temple tiles already placed on the board. Players play tiles and leaders onto the board, creating and expanding regions and kingdoms. Monuments are built on the board when four tiles of the same color are played into a square pattern.
Two leaders of the same type can not coexist in the same kingdom. Internal conflicts are caused by players adding a second leader of a type to a kingdom. External conflicts are caused by players playing tiles to merge two existing kingdoms.
During the game, players collect points in each of the four colors as a result of playing tiles, resolving conflicts and controlling monuments. After the final round each player sorts his or her points by color, including any "treasures" which they have acquired, which count as any color the player wishes. In order to limit specialization the player with the most points in their weakest category wins.
Players must balance their scoring and avoid overspecializing. Knizia later used this mechanism as the basis for Ingenious.