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Abstract. Up until recently, the applications of twistor theory to general relativity have been rather limited, applicable mainly to special solutions of the Einstein equations and to complex solutions which are anti-self-dual, these describing left-handed “non-linear gravitons”. Recently, however, a new approach-palatial twistor theory-has emerged which, though related to the earlier ambitwistor approach, is essentially different, bringing the quantum ideas of non-commutativity into the geometry. Though the (Einstein) space-times treated this way are still classical, the approach suggests a possible route to a quantum gravity theory.