 The fact that “NFU has no standard models” (the ordinals are not well-ordered in any set model of NFU) is a criticism of NFU which has merit. We observe, though, that there are other set theories in which nonstandard objects are deliberately provided (we will review some of these below), and some of the applications of those set theories to “nonstandard analysis” might be duplicated in suitable versions of NFU. We also observe that strong principles which minimize the nonstandard behavior of the ordinals turn out to give surprisingly strong axioms of infinity in NFU; the nonstandard structure of the ordinals allows insight into phenomena associated with large cardinals.