Calligraphy scripts are scripts derived from formal or nearly formal broad-pen forms. The most common of these are chancery cursives (the basis for italics that accompany many seriffed roman typefaces). Some, such as Poetica, are independent of romans. There are modern interpretations of chancery cursives that are looser than those of the Renaissance without being overly casual. Instances are Pouty or Medici Script. Other calligraphy scripts follow historical models such as rustics, uncials, Carolingian minuscule, humanist bookhands and rondes (an 18th c. French style). Among the uncials, which have no lowercase letters, are Omnia and Colmcille.
Blackletter types could be described as calligraphy scripts but because they have a long independent history, one that predates roman typefaces, they are placed in a separate category.