Crassus obliged handsomely. For the first seven years of his term in the east he squeezed the place dry as he had done back west, and indeed as was typical for governors; but as his term grew old he grew impatient and eager for glory, and invaded Parthia with the entire Syrian army (53 BC). The Romans had had no real disputes with the Parthians since Pompey had conquered Syria a decade before; Crassus was indifferent, and started the war anyways, confident that Pompey would force the Senate into declaring war for him. But despite his involvement in the defeat of Spartacus in 71 BC, Crassus was no real general; he marched his army straight at Parthia, across the least hospitable corner of Mesopotamia, and when the Parthians finally met up with him (at Carrhae, just barely across the actual frontier) he dug his soldiers in and held steady under endless volleys of Parthian archery. By the evening Crassus was dead, killed in an ill-planned attempt to negotiate, and the few survivors of his army had surrendered, handing over their standards and legionary eagles with them. It was the greatest Roman defeat since Cannae, but it had surprisingly little effect - the Persians were content with prying Armenia out of the Roman orbit, and Pompey and the Senate hastily disavowed Crassus' attack. Pompey and the Senate had issues closer to home to deal with, anyways: at the age of 42, and to the amazement of just about everyone, Julius Caesar had turned out to be the military genius of the age.
In 58 BC the tribe of the Helvetii**, pressed by German migration from their north and east, tried to cross into Roman Gaul. Caesar met them on the Saone river and defeated them decisively. The next year, on the grounds that they had supported the Helvetii, he defeated the Belgae in the north of Gaul***; the year after that, the Veneti in Brittany on the grounds of supporting the Belgae; the year after that, across the Rhine to shock and awe the Germans. In 54 BC he invaded Britain, more for the mystique of that semi-legendary isle than for any real strategic aim. In 53 BC the Belgae rose against the garrisons Caesar left behind and Caesar put them down again; in 52 BC the entire country rose under the great chieftain Vercingetorix. Caesar eventually trapped Vercingetorix at Alesia in central Gaul and after Caesar defeated the Gallic relief force Vercingetorix surrendered. In six years Caesar had conquered all of Gaul, written a memorably unmodest book about it, and made himself the hero of the Roman world.
Well, most of it. The Senate was now far more scared of Caesar than it had ever been of Pompey and Pompey was getting worried too - glory fades quickly and Pompey's great conquests were a decade gone, now. The Senate voted thanks to Caesar but no Triumph, as such a massive victory would normally have been due. This was a distinct mark of displeasure (or fear) but an even more obvious one was their demand after Caesar's governorship had expired (50 BC), that he disband his army and return alone to Rome. Caesar decided that this was the obvious prelude to arrest and execution that it looked like and in 49 BC crossed the Rubicon River into Italy at the head of his most loyal legion.
Pompey, still confident in his reputation, had promised the Senate that he need only stamp his foot and legions would arise to defend them; instead, troops flocked to Caesar. Pompey and the optimates fled in some disorder down the Italian peninsula and then to Greece. Caesar swung around into Spain****, defeated an optimas army there, then came back again to Greece; at Pharsalus (48 BC) he decisively defeated Pompey and his army. Pompey fled again, to Egypt, where the boy-Pharaoh Ptolemy XIII, fearful of sheltering the loser of the civil war, had him assassinated as he stepped off the boat. Caesar, following again, supported Ptolemy's sister and rival Cleopatra VII in her struggle for the throne anyways. The reasons are unknown but perhaps fairly obvious: Caesar's only known son (Ptolemy XV Caesarion) was with her.
The next few years saw Caesar crisscrossing the Republic, putting down optimas forces in the East (47 BC)*****, Africa (46 BC), and Spain again (45 BC). In the following year he returned to Rome and celebrated a Triumph for his victory in the Civil War. The Senate, somewhere between terror of him and gratitude for his quite general amnesty, elected him dictator in perpetuity - an unprecedented and illegal title, if hardly unexpected at this point. But if his amnesty and patronage of the populares' causes made him the idol of the people, it left many alive who still hated him for his overturning of the Republic. On March 15, 44 BC, in the midst of preparations for an expedition to Parthia to avenge Carrhae, a group of optimas senators surrounded him in the Senate building and hacked him to death with knives.
The assassins had hoped their tyrannicide would restore the Republic, but within days the anger of the mob, whipped up by Caesar's longtime lieutenant Marcus Antonius, had forced them from the city. The stage seemed to be set for a replay of the Civil War of 49-45 BC, with Antonius facing off against the last remnants of the optimates; in fact, there was still one player left to take the stage.
*The south of Gaul (still called Provence after its Roman nickname, "the Province") was technically largely run by the Greek city-state of Massilia (present-day Marseilles); but in practical terms Massilia was the most devoted imaginable client-state to Rome, and Caesar was able to run things there almost as smoothly as he did in his own province of Transalpine Gaul ("Gaul across the Alps"). Cisalpine Gaul ("Gaul this side of the Alps") was the Po valley, inhabited by Gauls before the Roman conquest. It was annexed to Italy in 42 BC, at the very end of the Republic.
**The latinate name for Switzerland, Helvetica, comes from the name of this tribe, but they were essentially unconnected to the modern Swiss; they were Celts just like the Gauls were.
***Belgium is named after them - a consciously neutral choice in a heavily divided country - but again they were Gauls with no distinct ethnic successors.
****En route he took Massilia, which had finally guessed wrong by supporting Pompey and was subsequently incorporated into Transalpine Gaul.
*****His conquest of Pontus in this campaign was the victory that came so quickly he dismissed it as "veni vidi vici" (I came, I saw, I conquered).