The yen as we know it is a modern creation. Before then, Japan had a series of currency systems that would make even Victorian Britons scratch their heads.
The ancient system
Before about 1600, Japan used a variety of coins. Much of the coinage in Japan during this era came from China: Chinese merchants would buy Japanese stuff in coin, and Japanese people would use the same coins to trade among themselves.
Besides Chinese coins, there were also coins minted by feudal lords (daimyo). In those bad old days, the only way to value these coins was by weighing them. The basic unit was the ryo, about 15 grams, which was subdivided into smaller units of weight: four bu to a ryo, four shu to a bu, four itome to a shu, and four koitome to an itome.
As in China, Japanese coins often had holes in the center so they could be carried on a string. This practice continues today in the 5-yen and 50-yen coins (although people usually carry them in their wallets nowadays).
The Edo-era system
Under the Tokugawa bakufu the coin system was standardized on a regional basis.
Around present-day Tokyo, trade was in gold coins, the largest of which was the one-ryo gold koban. Each koban was divided into four bu, and each bu was further divided into four shu. The value of a koban was roughly the same as the value of a koku of rice, the koku being the standard economic measure of pre-modern Japan. Occasionally, gold would be minted into huge coins called oban, which might be worth 10 koban (i.e. 150 g of gold), the kind of money you would only give someone for, say, conquering a province.
If you went farther west, around Osaka, trade was in silver coins measured by their weight in momme (1 momme = 3.75g). A koban's equivalent in silver was 50 to 60 momme, and a coin of that value was known as a cho. There were also bu and shu coins minted in the silver equivalent to their Tokyo values.
In addition to the gold and silver standards, small-scale trading was done in copper coins called mon. The exchange rate for copper varied between 4,000 and 10,000 mon to the koban. Daily wages, as well as prices for most everyday goods and services, would be in mon.
The old yen system
In the 1870s, Japan shifted from feudal government to parliamentary government, and adopted bimetallism as part of the modernization process. The yen became the official currency in 1871, having a value equivalent to the old koban. Each yen was divided into 100 sen, and each sen was divided into 100 rin. Yen coins for domestic trade were minted in gold, while yen coins for foreign trade were minted in silver.
During this decade, Japan created a number of national banks, each of which printed their own banknotes. In 1882, the national banks were replaced by a single Bank of Japan, which took over all currency printing and put the country on a silver standard.
In 1897, Japan switched to the gold standard. Japanese banknotes were convertible to gold until 1942, when Japan began printing money rather willy-nilly. During the war, Japanese coins appeared in aluminum and tin, and inflation got so bad that the sen and rin eventually became practically useless. Which is why, today, everything is denominated in yen, and a one-yen coin is light enough to float on top of a glass of water.
- Bank of Japan Currency Museum, http://www.imes.boj.or.jp/cm/english_htmls/history.htm