  In this thesis we have studied various applications of asymptotic Hodge
theory in string compactifications. This mathematical framework captures how
physical couplings of the resulting effective theories behave near field space
boundaries where the internal Calabi-Yau manifold degenerates. Below we
summarize the three parts in which this thesis is divided.
  Part I introduces the techniques from asymptotic Hodge theory we used
throughout this thesis. We review the results of the nilpotent orbit theorem of
Schmid and the multi-variable sl(2)-orbit theorem of Cattani, Kaplan and
Schmid. This discussion is tailored to applications in string
compactifications, explaining how to describe important physical couplings such
as K\"ahler potentials and flux superpotentials near boundaries in moduli
spaces.
  Part II discusses a geometrical application with the construction of general
models for asymptotic periods. Taking the constraints imposed by asymptotic
Hodge theory as consistency principles, we develop new methods for constructing
these periods. We explicitly carry out our program for all possible one- and
two-moduli boundaries.
  Part III discusses two applications of asymptotic Hodge theory in string
compactifications. The first investigates bounds put by the Weak Gravity
Conjecture in the setting of 4d $\mathcal{N}=2$ supergravity theories arising
from Type IIB Calabi-Yau compactifications. The second application studies flux
potentials in asymptotic regimes in complex structure moduli space, where we
develop two schemes for moduli stabilization. The first scheme sets up an
approximation procedure for finding flux vacua divided in three steps: the
sl(2)-approximation, the nilpotent orbit approximation, and the fully corrected
result. The second scheme constructs flux vacua with a small flux
superpotential by using essential exponential corrections controlled by
asymptotic Hodge theory.
