  Cosmic dust is present in many astrophysical objects, and recent observations
across the electromagnetic spectrum show that the dust distribution is often
strongly three-dimensional (3D). Dust grains are effective in absorbing and
scattering ultraviolet (UV)/optical radiation, and they re-emit the absorbed
energy at infrared wavelengths. Understanding the intrinsic properties of these
objects, including the dust itself, therefore requires 3D dust radiative
transfer (RT) calculations. Unfortunately, the 3D dust RT problem is nonlocal
and nonlinear, which makes it one of the hardest challenges in computational
astrophysics. Nevertheless, significant progress has been made in the past
decade, with an increasing number of codes capable of dealing with the complete
3D dust RT problem. We discuss the complexity of this problem, the two most
successful solution techniques [ray-tracing (RayT) and Monte Carlo (MC)], and
the state of the art in modeling observational data using 3D dust RT codes. We
end with an outlook on the bright future of this field.
