The transition to unsteadiness and the dynamics of weakly turbulent natural convection, coupled to wall or gas radiation in a differentially heated cubical cavity with adiabatic lateral walls, are studied numerically. The working fluid is air with small contents of water vapor and carbon dioxide whose infrared spectral radiative properties are modelled by the absorption distribution function model. A pseudo spectral Chebyshev collocation method is used to solve the flow field equations and is coupled to a direct ray tracing method for radiation transport. Flow structures are identified by means of either the proper orthogonal decomposition or the dynamic mode decomposition methods. We first retrieve the classical mechanism of transition to unsteadiness without radiation, characterized by counter-rotating streamwise-oriented vortices generated at the exit of the vertical boundary layers. Wall radiation through a transparent medium leads to a homogenization of lateral wall temperatures and the resulting transition mechanism is similar to that obtained with perfectly conducting lateral walls. The transition is due to an unstable stratification upstream the vertical boundary layers and is characterized by periodically oscillating transverse rolls of axis perpendicular to the main flow. When molecular gas radiation is accounted for, no periodic solution is found and the transition to unsteadiness displays complex structures with chimneys-like rolls whose axes are again parallel to the main flow. The origin of this instability is probably due to centrifugal forces, as suggested previously for the case without radiation. Above the transition to unsteadiness, at Ra = 3 × 108, it is shown that both wall and gas radiation significantly intensify turbulent fluctuations, decrease the thermal stratification in the core of the cavity, and increase the global circulation.