Was Abu Talib not a Muslim?

Abu Talib was the beloved uncle of prophet Muhammad (p.b.u.h.) and the father of Ali(p.b.u.h.). It is well known that how he protected and acted as a care-taker of the prophet from Quraysh . However, I heard that sunni Muslims consider him to be died as a non-muslim while shia muslims do not hold such and venerate him. ( Please correct/edit if any of what said above was wrong) **Question:** What are the sunni sources regarding their view and how reliable are these sources ? Similarly, What are the shia sources regarding their view and how reliable are these sources ?