Fishtail palms are famous for their uniquely shaped leaves. The fan-like, rough-edged foliage closely resembles the tail fin of a fish, which is where the name originates. These eye-catching palms are not winter-hardy and can only be grown outdoors in USDA zones 8 to 11, but they also make a statement as a large houseplant. Fishtail palms are frequently used in large areas like foyers and atriums, where they are planted in large pots. Once established, they grow fast, 1 to 2 feet per year.