  Over the last two decades, advances in fabrication have led to significant
progress in creating patterned heterostructures that support either carriers,
such as electrons or holes, with specific band structure or electromagnetic
waves with a given mode structure and dispersion. In this article, we review
the properties of light in coupled optical waveguides that support specific
energy spectra, with or without the effects of disorder, that are
well-described by a Hermitian tight-binding model. We show that with a
judicious choice of the initial wave packet, this system displays the
characteristics of a quantum particle, including transverse photonic transport
and localization, and that of a classical particle. We extend the analysis to
non-Hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians
which physically represent waveguide arrays with spatially separated, balanced
absorption or amplification. We show that coupled waveguides are an ideal
candidate to simulate $\mathcal{PT}$-symmetric Hamiltonians and the transition
from a purely real energy spectrum to a spectrum with complex conjugate
eigenvalues that occurs in them.
