There are three main types of people who collect money: those who collect paper money, those who collect coins, and those who collect both. Even though the things they collect are very different, they are mostly interested in the same things.
People collect paper money for many reasons, such as the chance of finding collectible bills from every country in the world. Many collectors will spend a lot of time learning about the country's history and how that type of currency came to be used during that time.
People who collect paper money have also learned that letting it sit in direct sunlight will cause it to fade and that Mylar is the best material to store it in. Polyvinylchloride (PVC) plastics may break down over time and take the paper with them. Money shouldn't be kept in window envelopes either, because light can get in through the window and damage the part of the bill that is showing.
Many people collect coins.
Coin collecting has been around for a very long time, and people save coins for many of the same reasons they save paper currency. A collector might want to have a coin from each year it was made and from each mint. They might also want to have a coin from each country that made it. The condition of a coin makes a big difference in how much it might be worth, and most collectors want coins that are in "mint" condition.
Like their paper counterparts, coins from the turn of the century are very rare and very valuable because of this. Many are now too expensive for a casual collector to buy. This could be one reason why people are more interested in collecting money from other countries.
Most collectible coins are kept in their own holders to keep them from getting scratches from other coins, which would lower their value. Then there are coin collectors who only do it for themselves and don't take their collections very seriously.
Serious collectors can use computer software to keep track of their collectible currency and write a short history of each piece in their collection. A collector can put in information about the item's history and how they got it, as well as what makes it collectible.
There are a lot of books about collectible currency, and most of them do a good job of explaining what makes each piece worth collecting and what to look for. The books also help set the price, but keep in mind that, like most collectibles, the price is set by what someone else is willing to pay.