In this chapter we give brief discussions of the main solution algorithms for radiation hydrodynamics problems, some of which are very quick and approximate and some of which represent the best attempts at accuracy. It is unfortunately true that “you get what you pay for” in these calculations, and accuracy comes at a considerable cost. The earlier material in this book has brought out quite a few different processes that complicate the endeavor, such as the effects of fluid velocity on radiation quantities, the complicated spectral dependence of the opacity, non-LTE, refraction, and polarization. These effects are not too hard to include singly, although with some effort, but accounting for all of them has not seemed to be a practical objective up to the present time. And of course these difficulties are compounded many-fold in higher-dimensional geometries. Our discussion of algorithms will begin with the low-budget methods that may be priced just right for many purposes, after some preliminary observations about solution strategy. Some general references on this subject are the following: The conference volume Astrophysical Radiation Hydrodynamics (Winkler and Norman, 1982) is a good place to start. A meeting that included presentations on many of the current advanced hydrodynamics methods was the 12th Kingston Meeting on Theoretical Astrophysics held in Halifax in 1996 (Norman, 1996). Starting points for surveying the advanced numerical methods in radiation transport are the pair of books by Kalkofen (1984,1987) and the workshop proceedings Stellar Atmospheres: Beyond Classical Models (Crivellari, Hubeny, and Hummer, 1991).