Roman soldiers learned how to do a lot of complicated movements so that they could fight better. One of the most famous was the testudo or "turtle", where all the soldiers used their shields to make a sort of shell all around the unit, as you can see in this carving from the Column of Trajan in Rome.
The Roman army fought many wars over the long history of the Roman Empire, and for hundreds of years they won pretty much all of their wars. In the early days of the Roman Republic, they beat the Etruscans, and then they beat the Greek city-states in southern Italy. By 275 BC the Roman army was fighting the First Punic War against Carthage, and then in 215 BC the Second Punic War: and again the Romans won both wars.
In the 100s BC, the Roman army fought in Greece and West Asia, and by the time of Augustus the Roman army had conquered Gaul (modern France), Greece, the whole Mediterranean coast of West Asia including Israel, and the whole coast of North Africa including Egypt. Augustus' step-grandson Claudius conquered Britain (England) about 50 AD.
By the 100s AD, Roman leaders were using swords made of crucible steel imported from India, but ordinary soldiers were probably still using iron swords. Trajan conquered Dacia (modern Romania) and large parts of Syria and Iraq about this time, but that was pretty much the end of Roman expansion. The Roman army spent more and more time putting down revolts like the First Jewish Revolt and the Second Jewish Revolt. To prevent invasions and revolts, the legions spent more and more time in one place, sitting on or near the borders to keep the empire safe. As they settled down, they began to put down roots: the soldiers married local women, inherited farms, and learned to speak the local language.
In the early 200s AD, the Roman army's situation took a turn for the worse. The Sassanian Persians in Iran and Iraq began attacking the Roman army along the West Asian border, hoping to push the Romans out of West Asia entirely. Seeing that the Roman army was busy in West Asia, a lot of other people living in northern and eastern Europe, like the Visigoths and the Ostrogoths, began to attack Rome as well, often coordinating their attacks so they would both attack at the same time. It was hard to fight two enemies at the same time.
By the 400s AD, the Roman emperors in the western part of the Empire didn't really have enough money to pay the soldiers anymore, and a lot of the soldiers found other things to do - farming, or fighting for other armies. The Roman army gradually faded away there, and the Visigoths and Ostrogoths moved in.
Science in Ancient Rome, by Jacqueline Harris (1998).