Trajan became emperor in 98 because the former emperor Nerva was forced to appoint him as succesor for being a popular general.
In 101-102 Trajan invaded Dacia, forcing king Decebalus to become a real Roman vassal after the Second Battle of Tapae.
In 105, king Decebalus revolted, killed the Roman garrison and raided Roman colonies across the Danube. At the same time, a confederation of tribes in northern Britain was founded out of the Caledonians and neighbours, called the Picts. The Picts raided Roman territory in 105.
Trajan's response was to give up parts of Roman Britain, mainly inhabited by the Votadini, and focused his atention on conquering Dacia, which was successful after the Battle of Sarmisegetusa in 106. The south of the Iazyges were conquered as well by general Hadrian.
In 106, king Rabbel II Soter of the Nabataean kingdom died. The Romans annexed his kingdom without a fight.
In 110, king Osroes I of the Parthian Empire placed Exedares on the Armenian throne, followed by Parthamasiris in 113, thereby encroaching the Roman right to be the overlord of Armenia. Trajan responded with an invasion of Armenia, which was annexed to the Roman Empire as a province. In 114, he gained the allegiance of the tribes of the Caucasus and along the coast of the Black Sea. In 115, Nisibis, a part of the Parthian Empire was annexed, to prevent Parthian interference into Roman Armenia.
In the meanwhile, the Kitos War started in 115 with a rebellion by Messianic Jews in Cyrenaica, who killed many Greeks in the area and destroyed Greek and Roman temples. Greek refugees from Cyrenaica started killing Jews in Alexandria, Egypt, in retaliation.
Trajan decided not to stop with a portion of the Parthian Empire and embarked on a campaign of full occupation, conquering both Parthian capitals, Ctesiphon and Susa in 116. The Jewish revolt broke loose in Alexandria, which was conquered by the Jews and depopulated. Also here, Greek and Roman temples were destroyed.
The Jewish revolt spread to the rest of Egypt and to Cyprus in 116, killing hundred thousands of Greeks and Romans. Also, the Jews in former Parthian Osroene and Mesopotamia revolted and the Parthians there as well. Trajan decided to focus on reconquering Egypt, Cyprus and Cyrenaica and maintaining the Roman position in Osroene and Armenia.
Trajan got sick in Mesopotamia and died on his way back to Rome in 117. In the meanwhile his generals Marcius Turbo and Lusius Quietus managed the reconquest of Cyrenaica, Egypt, Cyprus, Osroene and Armenia.