The youngest son of Ivan the Terrible, Dmitrii Ivanovich was banished by Boris Godunov after Ivan the Terrible died. After his body was found on May 14, 1591 many believed that Godunov in fact ordered the nine year old child to be murdered to ensure his election to the throne. Feodor 1 (another of Ivan's sons) ruled from 1584-1598, at which time he was succeed by Godunov, his brother-in-law.
In 1601, a man appeared who claimed to be Dmitrii Ivanovich. Over the years he gained great support, especially from the Polish who recognized him as Ivan's son and from the Cossacks. When Godunov died on April 13, 1605 his son Feodor was the successor.
It appears that in reality, this man was Grigorii Otrep'ev, a friend of the Romanov dynasty who came under suspicion during Boris Godunov's reign. Otrep'ev spent some years as a monk wandering from one monastery to another before beginning his campaign to be recognized as Dmitrii Ivanovich. Pushkin's play Boris Godunov (1824-25), later set as an opera by Mussorgsky, describes these events.
After his death, two more false Dmitriis appeared. The first in August 1607 continued to push his claim until he was killed in October, 1610. The second who appeared in March, 1611 was really a deacon named Sidorka, and was betrayed and executed.