During the Pleistocene, which began 2 million years ago, continental glaciers plowed into the Northeast and Upper Midwest; four glacial advances were separated by warm, interglacial periods, during which the ice sheets melted back into Canada. In fact, many climatologists believe that the Holocene, in which we live, is just another inter-glacial hiatus and that the ice will return within 5-10 thousand years.
Looking at a topographic map of North America, one can easily observe the flattened landscape that represents glaciated terrain. Stretching through western New York, western Ohio, the northern two-thirds of Indiana, Michigan, most of Illinois, northern Missouri, Iowa, Wisconsin, Minnesota and the eastern Dakotas, this province was plowed flat as the glaciers advanced and was coated with till as the ice sheets retreated. The Missouri River outlines the southern limit of glaciation to the west while the Ohio formed when the Teays River, which drained a broad swath from Virginia to northern Illinois, was blocked by ice.
Having scooped out the Great Lake basins as it plowed southward, the last Pleistocene glacier, the Wisconsin, filled them with meltwater as it retreated, some 12,000 years ago. With northern outlets still blocked by ice, the lakes spilled southward, forming and/or widening the river channels that we find today: the Susquehanna, the Great Miami, the Kankakee, the Wabash, the Illinois, the Upper Mississippi, the Minnesota and many smaller streams. Once the last glacier melted into northern Canada, the Red River and St. Lawrence River opened outlets to Hudson Bay and the Atlantic, respectively, and, combined with an upward rebound of the land, produced the drainage pattern that we find today. Current river and stream maps should be good until future glaciation, asteroid impacts or continental collisions readjust the terrain.