In late May and early June of 1863, General Ulysses S. Grant of the Union Army laid the city of Vicksburg, Mississippi to siege. This trapped a group of Confederate Army soldiers and their commander Lieutenant General John Pemberton in the city, with no way of getting supplies or any means of escape.
On July 4, Vicksburg surrendered.
This is considered one of the most brilliant military campaigns of the war, because it was a major turning point, giving control of the Mississippi River to the Union, effectively splitting the Confederate Army in half. This victory also led to Grant's ascension through the ranks to eventually becoming General-In-Chief of the Union armies.
Fun fact: General Grant spent most of his time in a cigar-induced haze as well as drunk, especially throughout the siege of Vicksburg. Also, the soldiers almost didn't make it through the siege, because they were camped in a swamp, which led to all sorts of water-damage related problems.
