Ontologies are descriptions of the knowledge about a domain of interest encoded in computer processable languages, e.g., Description Logics, which aredecidable fragments of First Order Logic. The main aim of ontologies is to define unambiguous vocabularies to facilitate knowledge sharing and integration.A critical issue with ontologies consists of their increasing complexity. To address this problem several notions of modularity have been recently proposed.Modularity notions can help in two ways: 1) If we know what sub-part of the ontology we want to work with, obtaining the appropriate module will allow us towork with that sub-part in a principled way; 2) a notion of module might induce a modular structure which allows users to explore the entire ontology in a sensiblemanner (perhaps finding appropriate sub-parts to work on). However, the most popular notion---locality based modules---while excelling at modular extractionhave thus far resisted attempts to induce a modular structure. Indeed, due their nature, locality based modules tend to occur in unfeasible numbers in ontologies.We tackle this problem by identifying basic building blocks of modules as sets of axioms which ``cling together'', that is, sets of axiom such that if any elementappears in a module, then all the rest due. This notion of an ``atom'' proves key to defining a useful family of locality based modular structures, the (Labelled)Atomic Decompositions ((L)ADs). In this thesis, we define (L)AD and explore its properties. We show that ADs are efficiently computable and, with appropraite labellings, provide a reasonably terserepresentation of the entire set of locality based modules. From ADs, we are able to distinguish so-called "genuine" modules, i.e., modules that cannot bedecomposed further as the union of two or more modules.Finally, we explore several of the applications to which (L)ADs have been applied including module extraction, ontology comprehension, and modular reasoning.