Perhaps originating north of the River Main, the Quadi and Marcomanni migrated into what is now Bohemia and Moravia, and western Slovakia, where they displaced Celtic cultures and were first noticed by Romans in 8 - 6 BCE, briefly documented by Tacitus in his Germania. A further Marcomannic confederation that included the Quadi fought the future emperor Tiberius in 6 CE.
Tacitus in Germania only mentions the Quadi in the same breath as the Marcomanni, alike in warlike spirit, alike governed by 'kings' of their own noble stock, 'descended from the noble line of Maroboduus and Tudrus,' the 'Tudric' line apparently kings among the Quadi. The royal powers of both tribes were also alike, according to Tacitus, in being supported by Roman silver.
Their frontiers for the next 350 years or more were the Marcomanni to the west, proto-Slavic tribes to the north, Sarmatian Iazgyians and (later) Asding Vandals to the east, and the Roman Empire to the south.
In the later 2nd century CE, Marcus Aurelius fought them in the Marcomannic War, for which our source is an abridgement of lost books of Dio Cassius' history. The troubles began in early 167 when the Langobardi Lombards and Obii crossed the Danube into Roman Moesia. They must have done so with the consent of the Quadi, through whose territory they had to cross. Presumably the Quadi wished to avoid trouble themselves by allowing these tribes to pass through into Roman territory. This invasion was apparently thrown back into Quadi territory without too much difficulty as far as the Romans were concerned, but the incursion marked the start of a long series of attempts to cross the border. A couple of years later the Marcomanni and Quadi, with assistance from other tribes that had crossed the Danube, overwhelmed a Roman army, passed over the plain at the head of the Adriatic and put the town of Aquileia in northern Italy under siege. After initial Roman losses, the Marcomanni were defeated in 171, and Marcus Aurelius managed to make peace with some of the tribes along the Danube, including the Quadi. But in 172 he launched a major attack into the territory of the Marcomanni and then turned on the Quadi, who had been aiding Marcomanni refugees. The Quadi were eliminated as a direct threat in 174. Marcus' planned counteroffensive across the Danube was prevented in 175, however, by insurrection within the Empire. Though Marcus Aurelius successfully suppressed the revolt, it was not until 178 that he was able to pursue the Quadi over the Danube into Bohemia. He was planning to advance the Roman border east and north to the Carpathian Mountains and Bohemia when he became ill and died in 180.
In the 4th century, Valentinian Valentinian spent much of his reign defending the Rhine frontier against a mixed horde of Sarmatians, Goths, and Quadi under their king Gabinius, who was slain at the treaty table by the Roman Marcellinus, son of the praefect of Gaul, Maximinus. Valentinian died in 375 CE after having received a deputation of Quadi to discuss a treaty. The insolent behavior of the proud barbarians so enraged the emperor, apparently, that he died of a stroke.
After about 400 CE the old cremation burials typical of Suevians like the Quadi disappear in Bohemia. The Quadi are among the mixture of peoples that evolved into the Bavarians.