The Roman study of Greek rhetoric started in Second Century (Appius Claudius Caecus is a name that often comes up)
Lost Works by Marcus Porcius Cato; Marcus Antonius (Antony's father); Quintus Hortensius
L. Plotius Gallus tried to form a truly "Roman" school of rhetoric c. 95.
Important also is the Rhetorica ad Herrenium, author unknown c. 86, sometimes ascribed to Cornificius; MSS ascribe to Cicero, but no one accpets that now. It translated and Romanized many Greek ideas and techniques; divides rhetoric into five parts: invention, arrangement, delivery, memory, and style.
Cicero important in transforming Roman rhetoric; the De Inventione is mostly traditional, but in his later works he criticises the mechanical approach of the Hellenistic methods. He also mediated the debate between the Asianists (like Hortensius) whose style was florid, ornate, and emotional, and Atticists (like Brutus) who style was restrained, moderate, and classical. Models of this style were Plato, Thucydides, Demosthenes. Cicero took Demosthenes as the model of oratory.
With the fall of the republic, oratory lost its vital place in a functioning government, and retreated to the schools, where it became more and more a matter of academic exercises called controversiae and suasoriae, which aimed at a declamatory style suitable for academic show-pieces.
Controversiae: something like todays "moot court", they are arguments on set, often absurd, moral, political, or legal situations. They were supposed to be designed to train for the courtroom, but many were too absurd. Seneca has a collection of these. The freely used sententiae and colores, "a plausible excuse or palliation of an offence" which often were outrageous....About the Vestal who survived being thrown fromt the Tarpeian Rock, he cites Junius Otho's color “Perhaps she prepared for her punishment and practised falling from the time when she began her offence.'" (OCD, s.v. color)
Suasoriae: the rhetorical speech of advice imagined as applicable to a crisis in the career of some eminent figure in hsitory (or mythology)...it involved for success historical knowledge, psychological penetration, and dramatic ability, e.g. “Alexander deliberates whether he should sail the Ocean,” "Cicero deliberates whether he should beg Anthony to spare his life" Ovid was good at suasoriae as a student (but not controversiae); he borrowed many of its techniques in writing his Heroides.
Quintilian in first century AD (Instituto) summed up the rhetorical theory of his day; and did for school rhetoric what Cicero had done for real rhetoric.