Born in New York, the West Point graduate of 1839 was an engineer, and earned some honors in the Mexican War. He also worked at fortifications, taught at West Point, and studied the French military. Because of his "scholarly pursuits", he earned the (later derogatory) nickname "Old Brains".
At the beginning of the American Civil War, he earned the rank of major general in the Union Army. He commanded the Department of the Missouri, Department of the Mississippi, and at the pinnacle of his military career, he became the commander in chief for two years (between 1862 and 1864). He was then relegated to chief of staff, after Lieutenant General Ulysses S. Grant was promoted to commander in chief. He held various commands of the James River after General Grant forced General Robert E. Lee to surrender at Appomattox Courthouse.
Although he was a gifted tactician and organizer, he was not aggressive enough in field campaigns. He effectively communicated President Abraham Lincoln's orders, but in his only field campaign (that of Corinth, Mississippi), he advanced at a very slow pace (about 1 mile a day), then entrenched. His subordinates' victories (especially those of Grant's) earned him his promotions, and he was rather effective in his position as chief of staff.
He died in Louisville, Kentucky, while commanding the Department of the South.