The coins of the Roman Republic prior to 241 BC are rare and expensive and therefore unlikely to appear on this website. However, for completeness, a rough chronology is listed below.
280-241 BC: Small numbers of gold coins.
280-211 BC: So-called "pre-denarius" silver coins based on those of Magna Graecia (the Greek colonies within Italy).
5th-4th centuries BC: "Aes Rude" - irregular lumps of bronze.
289-241 BC: "Aes Signatum" -large cast stamped ingots of bronze.
280-211 BC: "Aes Grave" - large cast bronze coins.
217-211 BC: "Aes Grave" -large struck bronze coins.
Finally in 211 BC the Aes Grave coinage was reformed and became a more recognizably bronze struck coinage, based on an "As".
Also in 211 BC, the basic silver unit of a denarius came into being, originally valued at 10 asses, later re-tariffed to 16 asses.
At the start of the Imperial period, around 18 BC, Augustus re-organized the currency system, including re-introducing a gold coinage. This was to last almost three centuries.
During the Imperial period, silver coins were struck in the Greek part of the Empire, based on the pre-existing coins, drachms and tetradrachms. Some cities (not just Greek) were also allowed to strike their own bronze coins, with or without inscriptions acknowledging imperial rule. Both types of coins are known as 'provincial' or Greek imperial'.
From the end of the first century, the denarius, the principal silver coin of the Empire was gradually de-based.
Around 215 AD, Caracalla (Antoninus) introduced a new silver coin, one and a half times the weight of the denarius and believed to be worth two denarii. One reason it is believed to be a two denarii coin is that the emperor's bust is wearing a radiate crown, often an indication that a coin is worth twice another (as with the dupondius which was worth 2 asses). If it had a special name it is not known and today is called an Antoninianus after Caracalla.
However, the coinage continued to be de-based and reduced in size. Aurelian (270-275 AD) reformed the coinage producing a new improved Antoninianus. These coins often had the mark "XXI" on the reverse, believed to refer to the metal content of ten parts of base metal to one of silver. The value of these coins compared with other denominations, especially the gold aureus is unknown, although there is plenty of speculation. The same goes for all the succeeding denominations. A confusion of different size coins follow making it very difficult to understand how each fitted into the system.
Aurelian's reforms seem to have been unsuccessful as Diocletian (284-305 AD) soon replaced the radiate coin with a much larger coin, known today as a follis. Even this fine coin soon degenerated and became smaller.
At this point we must call a halt to this description of denominations as any further comment would be speculation and would be so complicated as to require a complete book.
For the attribution of coins on this website, particularly for this late period, I have used denomination names given in David Sear's "Roman Coins and their Values". The one volume book (see Roman Reference Page) lists 'unknown' denominations by their size, such as AE2, AE3. The five volume series, which has so far reached four volumes replaces this nomenclature with actual names (specifically Volume 4). While this might be partly guesswork, it does provide a useful chronological background and the coins exhibited here use this convention.
All volumes of "Roman Coins and their Values" contain a chapter on denominations as well as further information within each book.