How did Romes political influence expand as it conquered new territories?

In the territories which were annexed, Rome was in charge. The provinces of the empire were administered by provincial governors. The local elites were allowed to run local affairs following local laws, customs and religions. Roman law regulated the affairs between Romans and locals. The governors acted as chief justices.. In the states which were allies or client states of Rome, the Romans intervened when there was political instability. The Romans built Roman towns around the empire to settle discharged veterans. These ex soldiers often married local women and played an important part in the spread of Roman influence. In the western provinces the Romans often linked aspects of their divinities with aspects of local divinities. Infrastructure projects (roads, bridges, aqueducts, baths, theatres, amphitheatres) and the thriving trading networks of the empire also played a part. Imperial propaganda was another factor.