What are the Medicinal Properties of Allspice (Pimenta Dioica)? Introduction Allspice is an evergreen tree which belongs to the Myrtle family. This tree grows in the tropical climate and can reach up to the height of 12m. This herb takes its name from the aroma it throws out as Allspice smells like a combination of many herbs, especially nutmeg, cloves, ginger, and cinnamon. This is the only spice to be grown exclusively in the western hemisphere. Allspice tree is indigenous