Abu al-Fadl Abbas, peace be upon him, was the brother of Imam Hasan [a] and Imam Husayn [a] and the standard-bearer of Imam Husayn [a] in the Battle of Karbala. He is well known in history for his valour, loyalty and similarity to his father, the Lion of God, Ali b. Abi Talib, peace be upon him.
The grave of Abbas [a] received similar attention as that of Imam Husayn [a]. In the year 1032 AH, the King Tahmaseb ordered the decoration of the grave's dome. He built a window on the 'darih' around the grave and organized the precinct. Other similar activities were done by other rulers.
As a matter of fact, Karbala contains, besides the grave of Imam Husayn [a] and his brother, the grave of all the 72 martyrs of Karbala. They were buried in a mass grave which was then covered with soil to the ground level. This mass grave is at the foot of Imam Husayn's [a] grave. In particular, besides Imam Husayn's grave are the graves of his two sons Ali Akbar and 6-month old Ali Asgher.
source : http://www.al-islam.org