||This dissertation identifies a strong computational property of phonological and morphological processes with local triggers. It is shown that the input-output mapping that underlies these processes can be modeled with Strictly Local (SL) functions, a previously undefined class of subregular relations. The SL functions, which are divided into two proper subclasses of subsequential functions (the Input SL functions and Output SL functions) are characterized in automata-theoretic terms by combining the properties of subsequential transduction (Mohri, 1997) and the Strictly Local formal languages (McNaughton and Papert, 1971; Rogers and Pullum, 2011; Rogers et al., 2013). Importantly, the property of strict locality is independent of and compatible with both rule- and constraint-based grammatical formalisms, since it holds of the input-output mappings that both formalisms describe. The range of processes that are shown to be Strictly Local includes substitution, deletion, insertion, synchronic metathesis, local partial reduplication, and general affixation. This computational property aids in identifying the set of 'phonologically possible' processes within the larger set of logically possible processes. In addition, a learning algorithm that provably learns the class of ISL functions by using strict locality as an inductive principle is also presented. These combined contributions to typology and learning demonstrate how computational analysis can enhance our understanding of the nature of locality in phonological processes.