The question of when the last Civil War veteran died is still a great controversy. On the Union side, it is fairly certain that the last veteran to die was Albert Woolson (1847-1956). He was with the 1st MN Heavy Artillery.
On the Confederate side, the generally accepted individual is Walter Williams (1842-1959). However, there is great doubt that Williams was born in 1842, or was even old enough to have been in the war. He may have been born as late as 1854. If Williams' claim is false, then there is John Salling (1846-1959). According to Census data, he was born in 1856, not 1846. The next claim was that of William Lundy (1848-1957), but his date of birth has also been questioned. If Salling and Lundy are false, then the last Confederate was Thomas Riddle (1846-1954).
If Riddle was the last Confederate, then Albert Woolson on the Union side was also the last Civil War veteran to die.
For whatever it is worth, the last known Union and Confederate widows of Civil War veterans died quite recently in 2003 and 2004.
The last Confederate veteran's widow died May 31, 2004 at the age of 97. Her name is Alberta Martin and she married the 81 year old William Martin when she was just 21! Her husband served with the 4Th Alabama Infantry Regiment and saw action at the Seige of Petersburg. He died in 1931.
The last known widow of a Union veteran was Gertrude Janeway who died in Tennessee in 2003 at the age of 93.