Aziridines, the smallest saturated aza-heterocycle, are not only prevalent in several natural products, but also represent a versatile synthetic tool for the chemist via exploitation of the strained ring system. Research described in this thesis concerns the chemistry of N-N ylides (aminimines), which were utilised in a novel tertiary amine-promoted organocatalytic approach to the aziridination of α,β-unsaturated carbonyl compounds. Through the use of modified conditions two important classes of substrates, dienones and alpha-enolizable enones, both of which had previously shown poor reactivity with the system, can now be aziridinated in good yields. Studies have also focused on the development of an asymmetric variant of the methodology using chiral tertiary amine promoters. A variety of novel chiral six-membered 1,4-heterocycles and cinchona alkaloid derivatives have been synthesised and their utility towards asymmetric alkene aziridination has been assessed, aiding the understanding of the proposed transition state model for the reaction.