In this review article we discuss recent constructions of global F-theory GUT
models and explain how to make use of toric geometry to do calculations within
this framework. After introducing the basic properties of global F-theory GUTs
we give a self-contained review of toric geometry and introduce all the tools
that are necessary to construct and analyze global F-theory models. We will
explain how to systematically obtain a large class of compact Calabi-Yau
fourfolds which can support F-theory GUTs by using the software package PALP.Comment: 19 pages. Prepared for the special issue "Computational Algebraic
Geometry in String and Gauge Theory" of Advances in High Energy Physics, v2:
references added, typos correcte
