A Brief History
In the 5th Century BC, the Aes Rude was used as coinage. It was cast bronze, in various shapes: squares, rectangles, and "lumps". Their weight made these too heavy for use as common currency.
The Aes Signatum followed, in the 3rd Century BC. These were cast with the images of animals, like birds and cattle, or objects, like shields. These were still too heavy to be considered true coinage. Imagine carrying around dumbbells as pocket change.
The Aes Grave was created (circa 289 BC) in several denominations: the As, Semis, Triens, Quadrans, Sextans, and the Uncia.
The Reverse image on all of these coins was a ship's prow. When flipping coins, "Heads or Ships" was the Roman equivalent of "Heads or Tails", a phrase which lasted long after the ship's prow was replaced by other reverse types.
This rudimentary bronze coinage was followed shortly by a silver coinage: a copy of the Greek silver Didrachm.
The first truly Roman silver coinage began around 211 BC. These included the Denarius, Quadrigatus, Victoriatus, and a silver Sestertius. Of these, only the denarius would survive into the Empire.
A common theme for early denarii was the head of Rome, wearing a helmet on the obverse, and somebody notable driving a chariot on the reverse. The chariot would normally be a biga (two horses) or a quadriga (four horses). See Page 1 for examples of Republican coins.
The vicissitudes of war and of expansion had their effect on Roman currency, and by the time of the Empire, a new system was in place.
The most common coins of the early Empire are the Denarius, Sestertius, Dupondius, and the As. The sestertius, no longer a silver coin, is the largest in size, with plenty of room for artistic expression. The dupondius usually portrays the emperor wearing a radiate crown, which, aside from its brassy colour, is sometimes the only way of distinguishing it from the as. The crown appears to indicate a "doubling" of the as.
The Later Empire
Values fluctuated through the years, until the denarius became so debased (i.e. becoming more bronze than silver) that a new coin was minted during the reign of Caracalla (211-217 AD) touted as a "double denarius". The exact name of the coin is unknown, but it is known today as an Antoninianus, and it featured the Emperor wearing a radiate crown. The antoninianus shortly took the place of the denarius, and in a few years became essentially a bronze coin itself. It was discontinued during the reign of Constantine the Great (308-337 AD).
At this time, the coinage went through more changes, and new coin types appeared to replace the old ones: the gold Solidus, the silver Siliqua, and the bronze (or copper) Follis. The name Centenionalis is also known for a small-denomination coin.
The Roman Empire included many regions and different races, languages, and beliefs. Many had their own pre-existing currency and economies.
Provincial coinage can be compared very loosely(!) to the modern euro. As the euro varies from country to country, the coinage varied from province to province, but more or less corresponding to the Roman system. Since there was no clear uniformity, provincial coins are often referred to by their size rather than as a specific denomination.