  Effective field theories provide a formalism for categorizing low-energy
effects of a high-energy fundamental theory in terms of the low-energy degrees
of freedom. This process has been well established in mapping the fundamental
theory of QCD in terms of the hadronic degrees of freedom, which allows for
quantitative connections and predictions between hardronic observables. A more
direct approach to performing the non-perturbative QCD calculations is through
lattice QCD. These computationally intensive calculations approximate continuum
physics with a discretized lattice to extract hadronic phenomena from first
principles. However, as in any approximation, there are multiple systematic
errors between lattice QCD calculation and actual hardronic phenomena. To
account for these systematic effects in terms of hadronic interactions,
effective field theory proves to be useful. However, the fundamental theory of
interest here is lattice QCD, as opposed to the usual continuum QCD. In this
work, the basics of this process are outlined, and multiple original
calculations are presented: effective field theory for anisotropic lattices,
I=2 $\pi\pi$ scattering for isotropic, anisotropic, and twisted mass lattices.
Additionally, a usage of effective field theories and the employment of an
isospin chemical potential on the lattice is proposed to extract several
computationally difficult scattering parameters. Lastly, recently proposed
local, chiral lattice actions are analyzed in the framework of effective field
theory, which illuminates various challenges in simulating such actions.
