Short answers, pulled from the story.
Roman interest in philosophy is first recorded in 155 BC, when Athens sent an embassy to Rome consisting of three philosophers: the Academic skeptic Carneades, the Stoic Diogenes of Babylon, and the Peripatetic Critolaus. Their visit introduced competing Greek philosophical schools to Roman audiences simultaneously.
The Stoic Opposition was a period during the Flavian dynasty when a group of philosophers, mostly Stoics, publicly protested against the actions of emperors Vespasian and Domitian. Vespasian responded by banishing all philosophers from Rome, with the exception of Gaius Musonius Rufus, who was later expelled as well. The term itself was not coined until the 19th century, first appearing in the writings of Gaston Boissier.
Marcus Aurelius chose to write his Meditations in Greek because Greek remained the prestige language of philosophical thought even during his reign as Roman emperor, which lasted until his death in 180 AD. He is counted among a small group of emperors, alongside Julian the Apostate, who are now regarded as philosophers themselves.
The School of the Sextii was an eclectic Roman philosophical school founded around 50 BC by Quintus Sextius and continued by his son Sextius Niger. It blended Pythagorean, Platonic, Cynic, and Stoic elements and emphasized nightly self-examination, vegetarianism, and avoidance of politics. The school went extinct in 19 AD when a ban on foreign cults dissolved it.
Neoplatonism, founded by Plotinus in the 3rd century AD, was initially used by non-Christians to attack Christianity. Christian thinkers including Augustine of Hippo, Boethius, and Eriugena later adopted its framework, making it a foundation of early Christian theology. Boethius, who lived from 472 to 524 AD, became the chief source through which Greek philosophical thought reached the early Middle Ages.
The two leading Roman law schools, the Sabinian and the Proculean, drew their ethical views from different Greek philosophical traditions. The Sabinian School aligned itself with Stoic readings while the Proculean School drew from Epicurean thought. This meant that the rivalry between two major Greek philosophical schools was replicated and extended into Roman jurisprudence.