| Summary: | In the introductory chapters I review this problem and recall how in IIB compactifications the dilation and complex structure moduli can be stabilised by 3-form fluxes. There exist very many possible discrete flux choices which motivates the use of statistical techniques to analyse this discretuum of choices. Such approaches generate formulae predicting the distribution of vacua and I describe numerical tests of these formulae on the Calabi-Yau ℙ<sup>4</sup><sub>[1,1,2,2,6]</sub>. Stabilising the Kähler moduli requires nonperturbative superpotential effects. I review the KKLT construction and explain why this must in general be supplemented with perturbative Kähler corrections. I show how the incorporation of such corrections generically leads to non-supersymmetric minima at exponentially large volumes, giving a detailed account of the α’ expansion and its relation to Kähler corrections. I illustrate this with explicit computations for the Calabi-Yau ℙ<sup>4</sup><sub>[1,1,1,6,9]</sub>. The next part of the thesis examines phenomenological applications of this construction. I first describe how the magnitude of the soft supersymmetry parameters may be computed. In the large-volume models the gravitino mass and soft terms are volume-suppressed. As we naturally have <i>V</i> >>1, this gives a dynamical solution of the hierarchy problem. I also demonstrate the existence of a fine structure in the soft terms, with gaugino masses naturally lighter than the gravitino mass by a factor 1n. A second chapter gives a detailed analysis of the relationship of moduli stabilisation to the QCD axions relevant to the strong CP problem, proving a no-go theorem on the compatibility of a QCD axion with supersymmetric moduli stabilisation. I describe how QCD axions can coexist with nonsupersymmetric perturbative stabilisation and how the large-volume models naturally contain axions with decay constants that are phenomenologically allowed and satisfy the appealing relationship <i>f</i><sup>2</sup><i><sub>a</sub></i><sub> </sub>~ <i>M<sub>P</sub>M<sub>susy</sub>. </i>A further chapter describe how a simple and predictive inflationary model can be built in the context of the above large-volume construction, using the no-scale Kähler potential to avoid the <i>η</i> problem.
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