We first review some basic results related to Serre's notion of G-complete reducibility for a reductive algebraic group G. We then discuss a relative variant of this concept where we let K be a reductive subgroup of G, and consider subgroups of G which normalise the identity component K° of K. We show that such a subgroup is relatively G-completely reducible with respect to K if and only if its image in the automorphism group of K° is completely reducible in the sense of Serre. This allows us to generalise a number of fundamental results from the absolute to the relative setting. This is a report on recent joint work with M. Gruchot and A. Litterick. [cite: 8, 14https://www.google.com/search?q=2]