As the creators of the series have always stated, they aimed for authenticity rather than accuracy. They enlisted the help of several historians and did quite an effort to recreate the Roman world, culture and habits into its tiniest details. The depiction of daily life, politics and warfare in Rome is therefore quite accurate, aside from some small issues (such as house decorations etc.) that still cause some controversy among historians.
The main story is also generally true. There was a long feud between Julius Caesar and Pompey Magnus that ended with Pompey's defeat, but Caesar was subsequently killed by his former enemies. In the vacuum of power, several groups kept fighting for the rule of Rome, which finally ended with the defeat and suicide of Mark Anthony and Cleopatra. The makers did, however, afford themselves quite some artistic licence with several historic facts and events, for the purpose of dramatic storytelling and to avoid unnecessary complexity.
The series greatly condenses the timeline of events and simplifies or alters both the politics and personal lives of people involved. For instance, Atia is depicted as a scheming, power-hungry vixen, which is quite contrary to historical evidence. She also lives through the entire series, whereas in reality, she died a year after Caesar, and was not present during most of the time depicted in season 2; Octavia, Atia's daughter, was never married to (and never divorced) a man called Glabius (as seen in season 1); she was married to someone else with who she had 3 children, all born after Caesar's death; the battle of Pharsalus was in reality preceded by the battle of Dyrrhachium, in which Pompey's army managed to defeat Ceasar's; The battle at Phillipi was not fought in one day; Cassius committed suicide during the first battle; Brutus was not killed either, he committed suicide after the second battle (although singly walking into the enemy's army could be considered suicide; his death by multiple swords was probably made to mirror Caesar's death); Brutus' mother Servilia did not commit suicide, she died a natural death (actually about a year after Atia's death); Mark Anthony already had two children with Cleopatra before he was married Octavia; he left Octavia to reunite with Cleopatra and have another child. Many of the real events have been moved in time to fit the time frame of the episodes better. For instance, Julia, Pompey's wife and Caesar's daughter, had already died years before the time depicted in the series; the siege of Alexandria already started before Caesar's battle with Ptolemy; and Cleopatra committed suicide 11 days after Mark Anthony's suicide.
Some accurate character traits known from historic sources made it into the show. Caesar was indeed of noble birth, but very popular with the commoners, also due to his habit of bribing people and being extremely merciful towards former enemies. Also correctly depicted is his brilliance as a general, being able to win several battles while being vastly outnumbered. Perhaps the most accurate characterization is that of Marc Antony, whom history describes as being a noted carouser as well as a brilliant general, and loyal ally to Caesar. His antagonism towards Cicero is also quite true; Cicero would described his disdain for Anthony, and wondered how someone of noble birth could be such a vulgar man.
Aside from altered facts, the writers inferred several facts for which there is no historical evidence (but technically no evidence against either). For instance, the secret relationship between Octavia and Marcus Agrippa, Mark Anthony's affair with Atia, the intensifying rivalry between Atia and Servilia, the incestual affair between Octavian and Octavia, Octavia's sexual relationship with Servilia, Servilia's active role in Caesar's assassination, Caesarion's escape from death, etc. The scene where Octavian helps cover up an epileptic seizure of Caesar's, which his mother mistakes for an affair between the two, is a combination of historical speculation that Caesar was an epileptic and an accusation from Marc Antony that Octavian had been Caesar's lover.
A completely fictionalised part of Rome is the entire Lucius Vorenus/Titus Pullo subplot. Vorenus and Pullo really existed, they are described by Caesar in his book De Bello Gallico (About the Gallic War) as rival officers. Everything aside from that (personal lives, historic roles, interaction with real persons) was created by the writers as a means to involve common men in the rich history and culture of the Roman Republic. The writers also invented Julius Caesar's slave Posca, his friendship with Caesar and his forced marriage to one of Octavia's friends.