The First Triumvirate began because three people were pissed at the Senate. Of course, it was very hard to find anyone in Rome who wasn’t pissed at the Senate, but these three decided to do something about it. The first fellow with anger management problems was Pompey. He’d gone out and conquered the Hispanians, Gauls, Iberians, Albanians, Phoenicians, Syrians, etc. but that wasn’t good enough for some people. Afraid that Pompey might decide to add Romans to his list, the Senate refused to recognize any of the treaties or rules he had laid down in Hispania, Gaul, Iberia and so forth. Somehow, this had the opposite effect they had hoped for.
Caesar got to hearing about this and offered Pompey a deal: You help me become Consul and I will help you to continue to do whatever the hell you want. Oh, and you can marry my daughter in the bargain (he’d heard Pompey had a knack for that). Caesar then turned to his other buddy Crassus who was rich as Midas and wanted to renegotiate taxes so he could become even richer. Oddly enough, the Senate was against that too. So really the Senators could only blame themselves when Caesar was elected Consul in 59 BC.
Pretty soon, Caesar discovered that being Consul was not as exciting as he thought it would be. And the Senate would keep nagging on about the slightest thing. It was enough to make him want to bash heads open. So he grabbed and army, had himself named proconsul, and headed out to Cisalpine Gaul (Northern Italy), Illyricum (the Balkins), and Transalpine Gaul (South France) where he bashed in heads to his heart’s content. (If you ever want to impress someone, tell them which side of the Alps Cisalpine Gaul is on. Or vice versa.)
Of course, eventually he was bound to run out of Cisalpine and/or Transalpine Gauls so Caesar moved north into Gallia Comata (we are near the end of the Gauls, I promise!) and began wreaking havoc there. A few illustrated texts under the name of Asterix and Obelix survive which recount the many perils the Romans faced against the plucky Gauls. In the end, however, Caesar triumphed and left Gaul in such desperate straits that there were no revolts against Roman rule (see Spartacus for a refresher on these). Caesar also cleaned up so much wealth that he was able to pay off all his debts and begin buying other political alliances.
Back in Rome, Pompey and Crassus shared the Consulship, and became increasingly irritated with each other. Soon, they were barely speaking to each other. A situation exacerbated by Crassus going east and getting himself killed by the Parthians in 53 BC. As Julia, had died in 54 BC (which was the year prior due to the peculiar habit the Romans had of counting backwards as they had not yet discovered years go the other way round) the Triumvirate was breaking up and Caesar was ready to take his act solo.