Short answers, pulled from the story.
Sextus Tarquinius was a son of Lucius Tarquinius Superbus, the last king of Rome. His rape of Lucretia is recorded in Roman tradition as the event that precipitated the overthrow of the Roman monarchy and the founding of the Roman Republic.
Sextus Tarquinius returned to Collatia, where Lucretia was the wife of his kinsman Tarquinius Collatinus, and entered her chamber at night with a drawn sword. He coerced her by threatening to kill her and a slave and frame her for adultery if she refused. Lucretia later sent word to her husband and her father Spurius Lucretius Tricipitinus, told them what had happened, and then killed herself.
According to Roman tradition, Sextus Tarquinius fled to Gabii after the rape of Lucretia and was killed there in revenge for his past actions against the town's people.
Shakespeare wrote extensively about Tarquin. The Rape of Lucrece is a narrative poem on the subject, long enough to take about two hours to recite. Shakespeare also alludes to Tarquin in Macbeth, Cymbeline, and Julius Caesar, using the name as a symbol of predatory stealth.
Titian painted Tarquin and Lucretia in 1571, Tintoretto painted the same subject around 1578, Rembrandt painted Lucretia in 1664, and Joos Van Cleve painted the Suicide of Lucretia between approximately 1520 and 1525.
Benjamin Britten composed The Rape of Lucretia, first performed in 1946. It is the most recent major operatic treatment of the ancient Roman story.