What are the virtues of the Prophet's صلى الله عليه وسلم grandchildren?

The virtues of the Prophet's grandchildren (peace and blessings be upon him) are the virtues of his Household (Ahl al-Bayt), and authentic hadiths have been narrated concerning them:

1. The Prophet's وصية (exhortation) to hold fast to the Book of Allah and his Household. 2. His (peace and blessings be upon him) saying: "I remind you by Allah concerning my Household." 3. The Household are the Book of Allah and the 'Itrah (offspring), and they will not separate until they meet me at the Hawd (Pond). 4. Whoever hates the Household will be cast into the Fire by Allah. 5. Allah chose the Prophet from Bani Hashim, and chose Bani Hashim from Quraish, and chose Quraish from Kinana. 6. Every lineage and relationship will be cut off on the Day of Resurrection except his (peace and blessings be upon him) lineage and relationship. 7. The revelation of the Verse of Purification concerning his Household (Hasan, Husain, Fatimah, and 'Ali). 8. Praying upon the Prophet and his Household is obligatory in the Tashahhud.