A general discussion of conformal vector fields in space-times is given. Amongst the topics considered are the maximum dimension of the conformal algebra for space-times that are not conformally flat, the nature of conformal isotropies and a new approach to the theorem of Bilyalov and Defrise-Carter concerning the reduction of the conformal algebra to a Killing or homothetic algebra. Some deficiencies in the original statements of this theorem are discussed (with reference to a general class of counterexamples) and corrected. The proof offered is geometrical in nature and has the advantage of displaying some of the more general features and properties of conformal vector fields and the ways in which they can differ from Killing vector fields.

The formalism developed by Fayos and Sopuerta for isometries in vacuum spacetimes is generalised in three ways: to include the case of homotheties, to allow for a tetrad not aligned to the symmetry structure and to allow for a non-normalised tetrad. The new formalism is used to recover results by McIntosh and also applied to the particular cases of Robinson-Trautman and Kundt type N.

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