Following the development, in the early 1970's, of the p-quotient algorithm for constructing polycyclic presentations of a finitely presented p-group, Leedham-Green and others developed an extensive family of elegant and efficient algorithms for finite p-groups. The facilities described here apply to the family of all finite p-groups defined by so-called power-conjugate presentations. Note that as p-groups form a subcategory of the category of finite soluble groups discussed above, most of the soluble group operations apply to p-groups. However, in some cases more efficient algorithms are employed for p-groups than for soluble groups.