  Twisted bilayer graphene (TBLG) has emerged as an important platform for
studying correlated phenomena, including unconventional superconductivity, in
two-dimensional systems. The complexity of the atomic-scale structures in TBLG
has made even the study of single-particle physics at low energies around the
Fermi level, quite challenging. Our goal here is to provide a convenient and
physically motivated picture of single-particle physics in TBLG using reduced
models with the smallest possible number of localized orbitals. The reduced
models exactly reproduce the low-energy bands of \textit{ab-initio}
tight-binding models, including the effects of atomic relaxations. Furthermore,
we obtain for the first time the corresponding Wannier orbitals that
incorporate all symmetries of TBLG, which are also calculated as a function of
angle, a requisite first step towards incorporating electron interaction
effects. We construct eight-band and five-band models for the low-energy states
for twist angles between $1.3^\circ$ and $0.6^\circ$. The models are created
using a multi-step Wannier projection technique starting with appropriate
$\textit{ab initio}$ $k \cdot p$ continuum hamiltonians. Our procedure can also
readily capture the perturbative effects of substrates and external
displacement fields while offering a significant reduction in complexity for
studying electron-electron correlation phenomena in realistic situations.
