In the US, we carry the same stuff in our wallets, pockets, purses, billfolds, etc. - there are dollar bills of varying denominations, quarters, nickels, dimes, and pennies. Occasionally a Canadian quarter or penny will find their way into the mix, but those are easily left for a tip or inserted into a vending machine.
Here in Belgium, my wallet has both US cash and Euros. I also carry a US credit card and a Belgian debit card. Euros are odd and I'm still learning to manage them. The euro notes get bigger as the amount gets bigger. Five euro notes are the size of Monopoly money. One hundred euro notes are much bigger than our dollar and are hard to stuff into a US wallet. There are only coins for 1 euro and 2 euros which means that my purse gets heavy. In addition to the penny we all know and love, there is a 2 cent coin - same color as a penny and only slightly bigger.
I have to not only remember what store takes what kind of money but also have a general idea of the current exchange rate (right now it takes about $1.32 to buy a euro).
At SHAPE, all the stores do business in euros. The post office takes only dollars. The American high school is dollar-based as well. The travel office takes only euros and only in cash.
At the US air force base, the P-Xtra, the PX and the Commissary are all dollars. I can pay with my US credit card at these places.
When we travel to England (hopefully before the end of the year) our dollars and euros are useless, for that we will need British pounds.
From where we live in Belgium we can be in a handful of other countries in a single day's drive. I can only imagine how much more complex this situation would have been before the change to the euro - how many wallets can one possibly carry?