Basil I (867-886 AD)
Basil took over as Roman Emperor in 867 AD, beginning what people call the Armenian Dynasty because of Basil's Armenian ancestors (Sometimes people call it the Macedonian Dynasty because Basil was born in Macedon). He continued basically the same policies as Bardas had, befriending the Bulgars and making sure that they were more friendly with Constantinople than with Western Europe. And he continued to send missionaries to Russia and the Serbs in the Balkans, so that they too became more friendly with Constantinople and more under Basil's power.
After Basil died in 886 AD from a hunting accident, power passed to his sons Leo VI and Alexander, who ruled together (as Caracalla and Geta had, for instance). Leo (who had most of the power) was not as good a general as his father, and sometimes lost battles with the Bulgars. In 904, he lost the Greek city of Thessaloniki to Abbasid attacks, and in 911 an attack on Constantinople itself by Russians from Kiev forced Leo to agree to Russian demands for free trade with Constantinople. Then when Leo tried to attack Crete and take it back from the Abbasids, he lost again. Leo died in 912 and then Alexander died in 913.
Constantine VIII and Zoe
When Alexander died, Leo's son Constantine VII became emperor, even though he was only seven years old. The Bulgars took advantage of the Empire's being ruled by a little boy to attack, and the regent, Nicholas, made peace with the Bulgars rather than fight them. This made him unpopular, and so Constantine's mother, Zoe, was able to get control and rule the Empire. But Zoe couldn't fight off the Bulgars either, and when Constantine was thirteen he was forced to marry a girl named Helena, so that her father Romanus could take over the real power.
It took Constantine until 944, when he was almost forty, to get power into his own hands and get rid of Romanus. But he didn't do any better - he tried to get Crete back, but failed again, and barely managed to fight off the Abbasid Empire's revenge attacks. By this time the Romans were paying tribute to the Bulgars to keep them from attacking. Constantine did invite Olga, a Russian princess, to visit and got her to convert to Christianity, and she went home and began to encourage the Russians to convert to Christianity too.
Constantine died in 959, when he was 53, and his son Romanus, who was 21, became emperor. Romanus finally succeeded in reconquering Crete from the Abbasid Empire, but he died young, in 963, when he was only 25 years old - people said he had been poisoned by his wife, Theophano, who became regent for their baby sons.
Now one of Romanus' generals, Nicephorus Phocas, became emperor - he was the general who had conquered Crete, so everyone liked him. Nicephorus married Romanus' widow, Theophano, and ruled alongside their baby sons. But he turned out not to be a very good emperor either - he just fought war after war with the Hungarians, the Bulgars, and the Abbasids, and this was so expensive that he had to raise taxes, which made him unpopular. Finally in 969 Theophano formed a conspiracy to kill him while he was sleeping.
Theophano's boyfriend, John, who was also Nicephorus' nephew, became emperor after they killed Nicephorus, in 969 AD. He was an aggressive general like his uncle, and won battles against both the Russians and the Abbasid Empire, expanding the Roman Empire into Bulgaria and much of Syria.
By the time John died suddenly in 976, Romanus and Theophano's son Basil II had grown up, and was able to become Emperor himself (although he was only eighteen!). Basil II turned out to be a much better emperor than his father or any of the other recent emperors. He forced rich men to pay their taxes again. He made an alliance with the Russian Czar Vladimir, where Vladimir helped Basil in war, and converted to Christianity, in exchange for marrying Basil's younger sister Anna. He also finished reconquering Syria from the Abbasids. But that's not all - Basil also reconquered most of the Bulgar empire, all the way to the Danube river, and pushed back the Hungarians too.