Short answers, pulled from the story.
Romulus and Remus were twin brothers born in Alba Longa to Rhea Silvia, a Vestal Virgin and daughter of the deposed king Numitor. Their story tells how they survived abandonment, overthrew the usurper Amulius, and set out to found a new city, a venture that ended with Remus killed and Romulus becoming the first king of Rome.
The image of a she-wolf suckling the infant twins in a cave known as the Lupercal became a symbol of Rome and the Roman people from at least the 3rd century BC. The twins and the she-wolf were also featured on what may be the earliest silver coins minted in Rome.
Remus was killed after a disputed contest of augury over which hill to build the new city on; Remus saw six auspicious birds and Romulus saw twelve. Depending on the source, Remus was killed either by Romulus himself or by a supporter named Celer. Ovid's Fasti records the ghost of Remus affirming that Celer acted alone and that Romulus still loved his brother.
The earliest known written account of the myth dates to the late 3rd century BC, authored by Quintus Fabius Pictor, who wrote his history of Rome in Greek. His work is now lost but was cited by Livy, Dionysius of Halicarnassus, and Plutarch, making it the foundation for most later accounts.
Roman historians dated the founding of Rome to around 753 BC, with estimates ranging between 758 and 728 BC. Plutarch reckoned the twins' birth year as 771 BC, placing the founding events several years later.
Current scholarship offers little evidence to support a historical Romulus or Remus. The archaeologist Andrea Carandini is one of the very few modern scholars who accepts them as historical, and he dates a wall on the north slope of the Palatine Hill to the mid-8th century BC, naming it the Murus Romuli. Most modern historians believe the name Romulus is a back-formation from the name Rome.