A numerical study was conducted to examine the structure and dynamics of steady, source-free spherical premixed flames ("flame balls"), which have been observed in microgravity experiments. A time-dependent spherically symmetric code was used with detailed chemical, transport, and radiation, submodels. Steady properties, stability limits, and dynamics of flame balls are computed for H-2-air mixtures. The chemical and radiation models used were found to affect flame ball properties substantially. The special and unusual role of thermal radiation from the combustion products is described. In particular, the far-field radiative loss is found to affect the behavior of flame balls in a manner very different from propagating planar flames. One new feature was identified: mixtures capable of exhibiting both stable flame balls and steadily propagating flames depending on the initial condition. Numerical results are compared to theoretical predictions, prior steady-state numerical calculations, and prior experimental results on flame ball size. Additional experiments were performed to measure flame bail radiant emission. Qualitative agreement with theory and experiment is found; however, quantitative agreement with experiment is only fair, indicating the need for improved microgravity conditions, e.g., in orbiting spacecraft.