Light has played an instrumental role in the initial development of the theory of
relativity. In this thesis, we intend to explore other physical phenomena that can be
explained by tracing the path that light takes in curved spacetime. We consider the
null geodesic and eikonal equations that are equivalent descriptions of the
propagation of light rays within the framework of numerical relativity. We find that
they are suited for different physical situations. The null geodesic equation is more
suited for tracing the path of individual light rays. We solve this equation in order to
visualize images of the sky that have been severely distorted by one or more black
holes, the so-called gravitational lensing effect. We demonstrate that our procedure
of solving the null geodesic equation is sufficiently robust to produce some of the
world's first images of the lensing effect from fully dynamical binary black hole
coalescence. The second formulation of propagation of light that we explore is the
eikonal surface equation. Because this equation describes the propagation of whole
surfaces of light, instead of individual light rays, we find it more apt in locating the
event horizon of a black hole. We will show that our solution method of the eikonal
surface equation to locate event horizons is also robust enough to find the event
horizon of a black hole that has accreted some negative energy density. While both
of these numerical simulations were able to achieve their basic goals for dynamical
spacetimes where solution by analytical methods is impractical, both simulations are
limited by computational requirements that we discuss.