Unlike other tubers and root vegetables, taro doesn't keep well for long periods. Taro roots will last for a few days if you store them in a cool, dark, well-ventilated spot. They won't do well in the refrigerator. The leaves, however, should go in the refrigerator. Wrap them in a damp paper towel inside a sealed plastic bag, and they'll also last for several days. You can freeze raw taro as well. First, boil it on high for five minutes, then let it cool and drain it. Pack it in a freezer bag and freeze immediately. If you have leftovers from your taro dish, they should go in the refrigerator or freezer within two hours. Cooked leaves can be frozen as well.