Symmetry properties of scattering amplitudes often lead to simplifications in their computation and in their final expression. Gluonic scattering amplitudes in pure Yang-Mills theory in the all-plus helicity configuration exhibit remarkable signs of conformal symmetry. At one-loop order they are found to be conformally invariant, but this observation still lacks an explanation. In the present thesis we analyze the conformal properties of all-plus gluon scattering amplitudes at one-loop order and present an attempt to rewrite them in terms of manifestly conformally invariant objects. This might lead to a better understanding of the origin of this symmetry for these amplitudes.