Sons of Heraclius
Heraclius' sons Heraclonas and Heraclius Constantine succeeded him when he died in 641 AD. They only lasted a few years. Heraclius Constantine died within the year, and his son Constantine (usually called Constans II) succeeded him, even though he was only 11 years old. Soon afterwards Heraclonas was also deposed, and the Empire was ruled by the advisors of little Constans. This did not make for strong leadership. But also the Empire was very weak. The Umayyads not only held onto the territory they had gotten: Syria, Lebanon, Jordan, Israel, and Egypt, they continued to add to it, working their way across North Africa to Carthage.
Mu'awiya on a Sassanian-style coin
The Caliph Mu'awiya realized that the Islamic Empire needed warships if it was going to conquer Constantinople, and he began building a fleet. Mu'awiya attacked the island of Cyprus first, in 649, to see if the Roman fleet was any good, and he succeeded in taking it. Mu'awiya also made successful attacks on the islands of Rhodes and Crete. Constans counterattacked but was badly defeated. But at this dangerous moment, the Umayyad dynasty began a civil war between Mu'awiya and Ali, and so they stopped attacking the Romans for a while (luckily for the Romans!).
Constans used the time to fight back the Slavs
in Greece, Serbia, and Bosnia, and he was more successful there.
To make sure his sons became emperor after he died, Constans tonsured his brother, Tiberius, and then later had him murdered just to be sure. But killing his brother, combined with unsuccessful military campaigns against the Lombards in Italy, made him unpopular, and he was assassinated in 668 AD when he was 37 years old. The rebellion was soon put down, and Constans' son Constantine IV became emperor.
Learn by doing: go out on a sailboat
More about Constantine IV