Short answers, pulled from the story.
The military history of ancient Rome is the account of the Roman state's armed forces and campaigns across roughly thirteen centuries. It is inseparable from Roman politics, which rested from an early date on competition within the ruling elite. Its core is the record of Rome's land battles, from the conquest of Italy to fights against the Huns and invading Germanic peoples.
From Gaius Marius and Sulla onward, control of the army became tied to the political ambitions of individuals. This fed the political triumvirate of the 1st century BC, which resolved in a civil war that brought the Republic's collapse.
At the highest level the Roman military was divided into the Roman army and the Roman navy. Within each branch, the actual structure changed substantially throughout its history.
The Roman army first fought tribal neighbors and Etruscan towns within Italy, then came to dominate much of the land surrounding the Mediterranean Sea. At the Empire's height its reach included the provinces of Britannia and Asia Minor.
The Crisis of the Third Century, dated 235 to 284 AD, was a period in the late empire shaped by usurpations led or supported by military conspiracies. It came amid the Empire's growing instability and eventual final decline.
Roman military technology ranged from sticks and stones to ballistae and quinqueremes. The siege is treated as a distinct topic within the military history of ancient Rome.