The chemistry of the tetrameric low-valent aluminium compoud (Cp*Al)4 (Cp* = 1,2,3,4,5- pentamethylcyclopentadienyl) is relatively undeveloped compared to its monomeric cousin dippNacNacAl (dippNacNac = 2,6-diisopropylphenyl-β-diketiminate). Given that the former can be formed by the reductive elimination of Cp*H from Cp*2AlH, a process common to transition metals yet rare with light main-group elements, using the Cp* ligand could unlock an abundance of unexpected reactivity for aluminium. An overview of the literature regarding the synthesis and reactivity of low oxidation state aluminium compounds is provided in chapter 1, as well as an introduction to relevant magnesium chemistry for this work. Chapter 2 studies the mechanism of C-H reductive elimination from Cp*2AlH to form (Cp*Al)4, and the properties which allow reductive elimination to take place are revealed. A transition state is identified where the Cp* group has a higher hapticity than in the starting material, a process which is thought to enable the reductive elimination. Using this insight, aluminium hydride and halide complexes featuring 9-methylfluorenyl ligands are synthesised and reduction of the aluminium centre is investigated. The reactivity of (Cp*Al)4 is considered in chapter 3 of this thesis. The formal cycloaddition reaction between (Cp*Al)4 and diphenylacetylene produces a Lewis acidic 1,4- dialuminacylohexadiene derivative. The inner Al2C4 ring of this complex is stable, with onward reactions happening at the complex's periphery. Insertion reactions in the Al-CCp* bonds are observed with unsaturated C-N species. With 2,6-dimethylphenylisonitrile the Al2C4 complex forms a zwitterionic aluminate, featuring a stable carbocation derived from the Cp* group. An amidinate complex with an unusual Cp* backbone is formed from the insertion of carbodiimides into the Al-CCp* bond of the 1,4-dialuminacyclohexadiene. Extending this, the insertion of carbon dioxide into the same bond is explored. The use of amidine ligands is common in main-group chemistry, however literature relating to the related phosphaamidinate ligands ([RPC(R)NR]-) is only reported sporadically. They have not been applied in a general manner to main-group chemistry thus far. Chapter 4 describes the synthesis of five new phosphaamidinate pro-ligands where the steric bulk of both the phosphorus and nitrogen components is increased systematically. To evaluate these new ligands, their coordination chemistry with magnesium was investigated. Three examples of heteroleptic LMgnBu (L = phosphaamidinate) complexes are synthesised, which all show high activity for the ring-opening polymerisation of racemic lactide. The resulting polylactide chains show good molecular weights and polydispersity indices. The synthesis of homoleptic L2Mg complexes is also described. Chapter 5 applies these new phosphaamidinate ligands to aluminium chemistry. An aluminium hydride species is isolated, which is shown to form via a probable lithium aluminate intermediate. The lifetime of this intermediate is found to be heavily dependent on the reaction solvent.