Constantine IV and Justinian
Constantine IV succeeded his father Constans II in 668 AD, with the Abbasids gradually taking over most of the eastern Roman Empire, and attempts to retake the western part ending in failure. Constantine IV was a strong and sensible emperor, who in 679 AD successfully defended Constantinople from its first Abbasid attack under the Caliph Mu'awiya. Constantine also tried to push back the Bulgars. He didn't succeed, and they established Bulgaria, which is still there today, but at least their settlement meant a lasting peace.
But Constantine IV died at 33, leaving his 16 year old son, Justinian, to succeed him. Justinian was smart and ambitious, but unfortunately, like his great-grandfather Heraclius, Justinian apparently suffered from mental illness. His paranoid persecutions led to a revolt in 695, and Justinian's nose was cut off and his tongue was slit before he was banished.
The new emperor, a mercenary soldier named Leontius, did nothing very well, and is remembered mainly for having lost Carthage to the Abbasids in 698. When that happened, his troops mutinied and replaced him with another soldier named Tiberius. Tiberius did pretty well, but then Justinian escaped and returned from exile, killing both Leontius and Tiberius. But Justinian was just as dangerous now as before, murdering and torturing people all the time, and in 711 AD he was killed, along with his 6-year-old son Tiberius. That ended the dynasty of Heraclius, and soon Anastasius II was the new emperor.