Recent results of the characterisation of the structure, morphology and orientation of fine-scale, strengthening precipitate phases in selected magnesium alloys using transmission electron microscopy and microdiffraction are reviewed. The strengthening precipitate phases in Mg-Y-Nd alloys, aged to maximum hardness at 250 o C, have been found to include two metastable precipitate phases β' and β 1 , and the equilibrium precipitate β. The β' phase has a globular form, a base-centred orthorhombic structure (potential point group of mmm), and an orientation relationship such that (100) β ' //(1210) α , [001] β ' //[0001] α . The β 1 phase has an f.c.c. structure (space group Fm3m), and an orientation relationship that may be described by (112) β 1 //(1100) α , (100) β 1 //[0001] α , and forms as plates parallel to {1100} α . The β phase has an f.c.c. structure (space group F43m) and also forms as plates on {1100} α , with an orientation relationship with the matrix phase that is identical to that observed for β 1 phase. Precipitates in Mg-Al alloys, aged isothermally at 200 o C, invariably have the b.c.c. structure of the equilibrium precipitate phase β (Mg 1 7 Al 1 2 ). Three orientation relationships have been observed between β and the matrix phase. Most precipitates have an irrational orientation relationship that approximates to the Burger's relationship, (001) β //(0001) α , [111] β //[2110] α , and a faceted lath morphology with habit plane parallel to (0001) α . A minor fraction of precipitates posses an orientation relationship that is of the form (110) β //(1100) α ,[111] β //[0001] α , and have a prismatic rod morphology. The long axes of these rods are parallel to [0001] α , and their faceted surfaces are parallel to {1100} α . A few precipitates are observed to have an orientation relationship such that (110) β ~//(1100) α ,[115] β ~//[0001] α and a rod shape, with their long axes apparently inclined with respect to [0001] α .