Short answers, pulled from the story.
The western theater encompassed Alabama, Georgia, Florida, Mississippi, North Carolina, Kentucky, South Carolina, and Tennessee, along with Louisiana east of the Mississippi River. Operations on the Gulf and Atlantic coasts of those states were generally assigned to the lower seaboard theater, while fighting west of the Mississippi fell under the trans-Mississippi theater.
The western theater lacked the proximity to the opposing capitals and major population centers that drew newspaper correspondents and public attention to the east. The fame of eastern generals such as Robert E. Lee and Stonewall Jackson further concentrated coverage on Virginia, even as Union forces in the west steadily dismantled Confederate resistance from 1861 onward.
Vicksburg surrendered to Ulysses S. Grant on the 4th of July 1863, and Port Hudson fell by the 8th of July, placing the entire Mississippi River under Union control and splitting the Confederacy in two. Combined with the Confederate defeat at Gettysburg the day before Vicksburg's fall, the capture is widely regarded as one of the war's turning points.
The Battle of Chickamauga, fought on the 19th and the 20th of September 1863 in northwestern Georgia, was the only major Union defeat in the western theater. A command misunderstanding opened a gap in the Union line that James Longstreet's corps exploited, sending the Army of the Cumberland into retreat to Chattanooga, where Braxton Bragg then besieged it.
Ulysses S. Grant rose to prominence in the west, winning at Forts Henry and Donelson, Shiloh, and Vicksburg before receiving command of all western armies as the Military Division of the Mississippi in October 1863. William Tecumseh Sherman succeeded Grant in that command and led the Atlanta Campaign, the March to the Sea, and the Carolinas Campaign. George H. Thomas commanded the Army of the Cumberland and directed the decisive victory at Nashville in December 1864.
Sherman's March to the Sea, formally the Savannah Campaign, began when his army left Atlanta on the 15th of November 1864 in two columns roughly 60 miles apart. Sherman applied scorched-earth principles, ordering troops to burn crops, kill livestock, and destroy civilian infrastructure, reaching Savannah by December and telegraphing Lincoln to present the city as a Christmas gift.