Everyone wants to know when and why the Roman Empire fell. This would be a surprise to medieval people, who assumed it was still in existence.
Historians, who like to break events up into periods, generally take "antiquity," which included the Roman Empire, as lasting until about 500 AD, and the Middle Ages as lasting roughly 500 to 1500. But of course no one woke up in 501 (anymore than they did in 1501) and discovered to their shock that everything had changed.
The year 500 is chosen because shortly before then (470s or 480s) there stopped being separate Roman emperors in Rome. Now in fact the Roman emperors had moved their capital to Constantinople, in what is now Turkey, 150 years or so before, in the early fourth century. (Sometimes after that there were two emperors, one in Rome and one in Constantinople, but usually just the one.) Even though there were no longer separate emperors in Rome, the Constantinople one sometimes stopped by Italy.
The real date for the "end of the Roman Empire" is 1453, when Constantinople fell to the Turks, which is why the region is now Turkey and the city Istanbul. Until then, there had been perfectly good Roman emperors.
But to get back to late antiquity, the other big change shortly before the year 500 was the establishment of new kingdoms within the Empire, made up of Germanic peoples, especially the Goths and the Franks. One sometimes hears about "hordes of Germans" destroying the Empire, but this is not true. These Germanic peoples wanted to be Roman. Clovis, king of the Franks (d. 511), now considered the "first king of France," wore a toga, wrote away to Constantinople to get a special medal of recognition, converted to Christianity (a Roman religion), and had the traditional laws of his people written down in Latin, in imitation of Latin law codes. France speaks French now, a language derived from Latin, because the Franks immediately jettisoned their native tongue for the language of the Empire.
The Empire had been having problems of its own for several centuries, primarily because its economy was based on constantly capturing new slaves in war and working them to death, and they had stopped winning their wars. The Franks (as well as the Goths, doing basically the same things in Spain) provided a jolt of energy. Pictured above is a reproduction of a Frankish belt buckle, depicting a rider (I wear it as a pendant).
The Empire received a nasty setback in the middle of the seventh century, with the rise of Islam, which took over much of the Middle East, all of north Africa, and Spain. Most of Continental Europe, however, sought to maintain its Roman traditions.
Eventually a Frankish king, Charlemagne, was crowned Roman Emperor in 800, meaning there were two emperors once again, but that's a story for another post.
By the way, probably the reason one hears about Germans overpowering the Roman Empire like tides roaring into the Bay of Fundy is because something almost like that did happen in Britain, where Angles and Saxons overwhelmed the Romanized Celtic population. But Britain and the Continent were and are different (ask any Brit).