In this article, we identify Strict Locality as a strong computational property of a certain class of phonological maps from underlying to surface forms. We show that these maps can be modeled with Input Strictly Local functions, a previously undefined class of subregular relations. These functions extend the conception of locality from the Strictly Local formal languages (recognizers/acceptors) (McNaughton and Papert 1971, Rogers and Pullum 2011, Rogers et al. 2013) to maps (transducers/functions) and therefore formalize the notion of phonological locality. We discuss the insights such computational properties provide for phonological theory, typology, and learning.