  This thesis is divided into two major parts. Part I provides an overview of
some of the most important formalisms of transport theory, while Part II
provides a presentation and discussion of my own work. The order in which these
parts are read is not important, as long as the reader is prepared to accept
that part II references a few topics in part I.
  Part 1 discusses 6 different theoretical frameworks: The Landauer B\"uttiker
framework, the Keldysh field integral, linear response theory, Non-Equilibrium
Green's function (NEGF) formalism, Markovian Master equations, and the semi
classical Boltzmann equation. Considerable weight is put on illuminating the
connections between these frameworks, and in particular an attempt is made to
derive all of the latter four as a sequence of approximations starting from the
Keldysh field integral, admittedly with some appeals to physical intuition.
  While part 1 is mostly concerned with fundamental theory, the focus of part 2
is on computational and numerical aspects. It discusses a set of practical
calculations we have made, using a subset of the formalisms from part 1. In
particular, we have made use of the Boltzmann Monte Carlo method to solve the
Boltzmann equation, applying both direct calculations and the Green Kubo
relations of linear response. We have also made some calculations in the
Landauer B\"uttiker framework, utilizing B\"uttikers approximation to introduce
scattering in an otherwise ballistic solver. Finally, we have performed a set
of calculations within the NEGF framework, which illustrate a simple
perturbative approach useful for speeding up the calculations of Gr, as well as
a Monte Carlo method developed of our own.
