The dyadic Green's functions in three dimensions are constructed for a general uniaxial medium. This is a structure whereby the presence of a distinguished axis introduces an anisotropy into the constitutive relations of the medium. All four dyadic Green's functions (which are of the electric, magnetic and mixed types) are given and some of their properties (for example, symmetries) are discussed. By specifying the source to an electric dipole it is shown how singularities of the Green's functions have to be treated. The presented results can be applied to magnetised plasmas, magnetised ferrites and other substrates for microwave and optical devices as well as for moving isotropic media.