Initially a small hellenised city state in the Italian peninsula, Rome slowly overwhelmed its Latin neighbours and later the southern Greek cities after surviving a brutal invasion from Pyrrhus of Epirus, taking complete control of the peninsula.
Rome then was then engaged in three Punic wars with the maritime trading city of Carthage. The first of these bloody wars brought Sicily under complete Roman control, along with Sardinia and Corsica. The second and most important Punic war featured Hannibal's invasion of Italy, and through tactical genius he defeated them several times, most famously at Cannae. However Roman defiance ensured the state was pulled back from the brink of destruction and soon armies under Scipio Africanus secured Spain, then invaded Africa. The weary Hannibal was then soundly defeated at Zama, and Carthage sued for peace. The third Punic war after a brief struggle annialated the city of Carthago itself.
From there Roman power was unanswerable and major kingdoms and celtic tribes were subdued. The republic collapsed when Caesar turned on the capital, but continued under the Principate, a monarchy in all but name.
Roman rule ended in the third century B.C, it's military a shadow of its former self, and the ancient republican traditions abandoned. However, the Eastern Empire continued until medieval ages with it's capital at Byzantine or Constantinople.
The Romans are respected for being the founders of modern day democracy, and their military, architectural, social and administritive prowess. The collapse of the Roman empire brought about a dark age and under Europe plunged into the bloody medieval ages, setting back human advancement by hundreds of years.
(It is thought the bible was formulated initially by Constantine, and Christianity spread through the Roman Empire - hence purist Roman Catholosism exists today. Pagan my arse.)
The Roman Empire stretched from Spain to Syria, including the largest variety of cultures ever seen before, lasting at its largest point for four centuries.