The Roman Empire included most of what would now be considered Western Europe. The empire was conquered by the Roman Army and a Roman way of life was established in these conquered countries. The main countries conquered were England/Wales (then known as Britannia), Spain (Hispania), France (Gaul or Gallia), Greece (Achaea), the Middle East (Judea) and the North African coastal region.
In Rome's early years, the state lived in fear of its more powerful neighbour, Carthage. The Carthaginians were great traders in the Mediterranean Sea and as the Romans wanted to expand into this trading zone, a clash was inevitable. In 264 BC, the Romans and the Carthaginians had their first war. In a series of three wars, known as the Punic Wars, the Romans eventually defeated the Carthaginians. However, this took over 100 years to accomplish and the wars eventually ended in 146 BC. In the second Punic War, the Romans lost several important battles - the most famous being against the Carthaginian general Hannibal. However, by 146 BC, the Romans were strong enough to capture the city of Carthage in Northern Africa. Carthage was burned to the ground and all signs of the city were destroyed by the Romans as a sign that the power of the Carthaginians had disappeared forever.
With Carthage defeated, the Romans became the most powerful Mediterranean state. The victory over the Carthaginians gave the Romans all the opportunity they needed to expand their power in the Mediterranean. The more wealthy and powerful the Romans became, the more able they were to further expand their empire.
The Romans were not content with conquering land near to them. They realised that land further away might also have riches in them that would make Rome even more wealthy. Hence their drive to conquer Western Europe. At the height of its power, around AD 150, Rome controlled the greatest empire ever seen in Europe at that time. Many of the conquered nations benefited from Roman rule as the Roman way of life was imposed on those conquered societies. Roman public baths, roads, water supplies, housing etc. all appeared in Western Europe - though many fell into disuse after the Romans retreated back to Rome.
Ironically, the sheer size of the empire, which many marvelled at, was also a major reason for the collapse in the power of the Romans. The Romans had great difficulty in maintaining power in all of their empire and supplying their army was a major problem as their lines of communications were stretched to the limit. The power of the empire rested with the success of the Roman Army. When this success started to weaken, the empire could only start to collapse.