What happened after Veii?

In 396BC the City of Rome attacked the City of Veii. The Romans won. Up until that battle, the Etruscans had been dominant in Northern Italy.

A few years later, the Gauls attacked Rome in the Battle of Allia in 387BC. The Romans at first were being defeated but with the arrival of reinforcements were eventually victorious. After that the Romans restructured there Army and were for a time the dominant armed force in Italy.

At some stage, the Etruscans disappeared. For the Gauls to have reached Rome, they must first to have passed through Etruscan dominated Italy. Did they conquer it? Did the Romans conquer it? What happened?