The initial aim of this thesis was to apply and extend the chemistry of pyrrolizin-3-one ring systems to the synthesis of naturally occurring pyrrolizidine alkaloids. The methods of synthesis of unsubstituted-, 1-monosubstituted-, 7-monosubstituted- and 1,7-disubstituted pyrrolizidin-3-ones have been reviewed. Many pyrrolizin-3-ones have been synthesised by Flash Vacuum Pyrolysis (FVP) of propenoate ester derivatives or Meldrum's acid derivatives. A new synthetic route to pyrrolizin-3-ones substituted at the 1-position by electron-withdrawing groups has been developed by FVP of Wittig condensation products from pyrrol-2-ylglyoxylic acid derivatives. Unexpectedly 1-methoxycarbonylpyrrolizin-3-one spontaneously dimerises at room temperature within two days, in contrast to all other pyrrolizin-3-ones which are known to be stable. The dimerisation is thought to take place via a captodative diradical intermediate. Hydrogenation of 1- and 7-monosubstituted pyrrolizin-3-ones proceeds smoothly to give the perhydro system with very high diastereoselectivity after optimisation, in particular from the 7-monosubstituted pyrrolizin-3-ones. The level of selectivity attained is greatly dependent on experimental conditions, namely catalysts and solvents. Hydrogenation of 1,2-dihydro-1, 7-disubstituted pyrrolizin-3-ones is more complex due to addition steric interactions but some degree of diastereoselectivity is nevertheless observed. Reduction of the pyrrolizidin-3-one systems thus obtained allowed the synthesis of the pyrrolizidines heliotridane, isoretronecanol (both by two complementary routes) and retronecanol. Cycloaddition reactions of 1- and 2-monosubstituted pyrrolizin-3-ones with isobenzofuran have been studied. High selectivity for the endo products has been observed for pyrrolizin-3-one itself and the 1-methoxycarbonyl derivative, possibly due to a stabilisation of the transition state by favourable secondary orbital interactions. The methodology was then applied to the synthesis for the natural product pyrrolam A in three steps from pyrrolizin-3-one by a Diels Alder - hydrogenation - retro Diels Alder sequence. The rate of ring opening of a variety of monosubstituted pyrrolizin-3-one by reaction with sodium methoxide was followed by Stopped Flow kinetics. The rate was found to be greatly dependent on the nature of substituents and to a less extent on their position. The results have been applied to the synthesis of cis-urocanic acid in two steps from methyl (E)-3-(imidazol-4-yl)propenoate. Finally extension of the chemistry of pyrrolizin-3-ones has been briefly investigated, in particular reactions with organolithium derivatives and thiophenol, oxidation and reduction reactions and photochemical dimerisation.