U.S. coin collecting has grown in popularity since the 1850s, while ancient coin collecting has been a popular hobby for centuries worldwide. European monarchs and even popes have assembled impressive collections since medieval times (and ancient coin reference books date back to the 1500s).
Many people shy away from collecting ancient coins because they think they are complicated. But ancients are the basis for all modern coinage - the majority have an obverse and reverse design. And Roman Imperial coins have portraits, making them very similar to U.S. coins. Most collectors choose coins based on obverse designs, but some enjoy collecting various reverses.
While it is possible to collect coins from nearly all of the Roman emperors, some are difficult to find because the emperors only ruled for a short time. Usurpers and self-proclaimed rulers also struck coins, and many of these are quite rare.