The assassination would unite Octavian and Mark Antony against Brutus and Cassius in the Liberator's Civil War, the defeat (and suicide) of Cassius in the First Battle of Philippi, and the defeat (and suicide) of Brutus in the Second Battle of Philippi just 2 years after Caesar's murder.
Octavian would return to Italy while Antony would stay in the East. The alliance didn't last, and in 31 BC, Octavian defeated Antony and Cleoptara in the Battle of Actium.
Brutus and Cassius set out to prevent Caesar from becoming king. In the vacuum he left, Octavian became Rome's first emperor, dubbing himself Caesar Agustus.