Radiative transfer is at the heart of the mechanism to explain the greenhouse effect due to carbone dioxide, methane and others in the earth atmosphere. We revisit this much studied field from a mathematical and numerical point of view. Existence and uniqueness and semi-analytic solutions of the Milne problem for grey atmospheres are stated. Numerical simulations are given for grey and non grey atmosphere and applied to the greenhouse effect. It is found that greenhouse gases are indeed capable of making the earth temperature 1 − 2 o C hotter, even without taking into account the complexity of full ocean-atmosphere-chemical climate models.