(My answer on Quora)
He died of typhus in December 1825 and since he had no legitimate heirs (his two daughters died in childhood) a succession crisis following his passing. This was complicated by the military supporters of the Decembrist revolt who favored Tsar Alexander’s earlier liberal reforms. The revolt failed and the Tsar was eventually succeeded by his reactionary brother Nicholas I.
It is worth noting that Alexander I ruled between 1801–1825. He was the same Tsar that helped turn Napoleon’s 1812 invasion of Russia into a disaster for the Corsican. Although Alexander introduced reform in the early part of his reign he became increasingly despotic in the latter portion of his life and was dominated by a religious zealotry that was becoming increasingly regressive. Rumors persisted after his death that he was actually alive and was living as a hermit in Siberia. This hasn’t been substantiated.