When Domitian came to power he did so with a great family pedigree of military success. Vespasian had proven himself in Britain, Germania and the east while Titus experienced similar conditions and continued his father's work in Judaea.
Much like the reign of Claudius, who needed the conquest of Britain to legitimize himself, Domitian felt the need to prove his own military prowess. While his initial attempts to accomplish that are scoffed at by Suetonius, Tacitus and Dio Cassius (in reference to the later Dacian Wars, Dio indicates that Domitian spent his campaign time indulging in riotous living far from the front) they served the purpose of glorifying his own young reign and uniting the legions behind him.
Domitian's first opportunity to realize military success came as the result of a ruse. Moving to Gaul in AD 82 under the pretense of conducting a census, Domitian instead recruited a new legion, Legio I Minervia, and moved with it and others into the Agri Decumates (the upper Danube and Rhine area) to conduct a campaign against the Chatti. While this initial attack had the intention of completing the conquests begun by his father, Domitian's efforts largely consisted of road building, fortification and the like. Domitian returned to Rome in AD 83 to celebrate a triumph, claiming the title Germanicus in the process. Despite his apparent victory, the Chatti were far from defeated and would continue to resist for another 6 years, lasting into AD 89 when the Romans eventually pushed the Empire's frontiers to the rivers Lahn and Main. While Domitian's triumph was largely an effort to boost the emperor's popularity (accompanied by a 1/3 pay raise for the legions), its effect was not wasted and would serve the emperor well into the future.
Meanwhile in Britain, the efforts of Governor Gnaeus Julius Agricola were not going unnoticed in Rome. Having been appointed to the command of the frontier province under Vespasian (AD 78), his tenure included the subjugation of several resisting tribes in a methodical drive to the north. By AD 81 Agricola had pushed into Caledonia (modern Scotland) and was allowed to keep his position as Domitian came into power. According to Agricola's son-in-law, the historian Tacitus, Agricola reportedly even considered an invasion of Ireland that he claimed could be accomplished with just one legion. (It's important to note here, that some hostility from Tacitus towards Domitian can be accredited to Domitian's later treatment of Agricola and perhaps did have an impact on Tactitus' overall portrayal of him as the Emperor.)
In AD 83, Agricola won a smashing victory over Caledonian resistance, led by Calgacus, at the battle of Mons Graupius opening the way to Roman dominance of the entire island province. Fortifying his position at such places as Chester and Caerleon, Agricola's fleet explored the Orkney Islands and coastal borders, proving that Rome's northernmost province was indeed an island. The following campaign year would likely bring further incursions into the Caledonian highlands, however, Domitian recalled his successful general in AD 84. Accused of jealousy in the wake of Agricola's success, in light of his own trumped up triumph regarding the Chatti expedition, arguments have been made the Agricola may have completed the conquest of all of Britain. While Agricola was offered triumphal rewards, his relegation into obscurity and lack of further posts fueled speculation that Domitian was either jealous or mistrustful.
As the situation along the Danube with the Dacians began to worsen in the mid 80's, the conquests in Caledonia became an afterthought. Despite the security provided by holding the 'Scottish Lowlands', Domitian began the systematic withdrawal of Agricola's fortifications in AD 86 and 87. The defeat of Cornelius Fuscus and 2 legions to the Dacians precipitated the transfer of troops to the Danube and Caledonia, a territory with minor strategic priority and lacking any financial reward for the Empire, became dispensable. Though Tacitus complained of betrayal and surrender, the deed was done, and no Roman would ever hold as much territory in Caledonia, despite several later efforts, as did Agricola. While Agricola was left to fade into obscurity (his death in AD 93 was rumored to be at Domitian's bequest), Domitian was forced to focus attention on the restless Danube.