In a standard formulation of the renormalisation group (RG) a renormalised covariant gauge parameter is just as much a running parameter as are couplings and masses. In the past, by working in the Landau gauge, issues associated with a running covariant gauge parameter have largely been avoided. The present author looks at the main consequences of maintaining a general covariant gauge. He also reviews Gross' fixed gauge RG (1976) in which there has been renewed interest. For physical amplitudes this provides a simpler alternative to the standard RG. However, he shows that the fixed gauge RG invariants are in fact gauge dependent. Finally he points out that the Cell master-Gonsalves relation (1979) is only true for the fixed gauge RG and not the standard RG. One may use this fact to extract the explicit gauge dependence of the fixed gauge RG invariants.