The Battle of Cold Harbor was fought from May 31 to June 12, 1864, with the most significant fighting occurring on June 3. It was one of the final battles of the Overland Campaign, and is remembered as one of American history's bloodiest, most lopsided battles. Thousands of Union soldiers were killed or wounded in a hopeless frontal assault against the fortified positions of General Lee's army. On May 31, Union cavalry seized the crossroads of Old Cold Harbor, about ten miles northeast of the Confederate capital of Richmond, Virginia, holding it against Confederate attacks until the Union infantry arrived. Both Grant and Lee, whose armies had suffered enormous casualties in the Overland Campaign, received reinforcements. On June 2, the remainder of both armies arrived and the Confederates built an elaborate series of fortifications. At dawn on June 3, three Union corps attacked the Confederate works on the southern end of the line and were easily repulsed with heavy casualties. Attempts to assault the northern end of the line and to resume the assaults on the southern were unsuccessful. In the final stage, Grant alternated between digging into the trenches at Petersburg and fleeing westward across Virginia.