We present a model for the diffuse interstellar dust that explains the observed wavelength-dependence of extinction, emission, and the linear and circular polarisation of light. The model is set up with a small number of parameters. It consists of a mixture of amorphous carbon and silicate grains with sizes from the molecular domain of 0.5 up to about 500 nm. Dust grains with radii larger than 6 nm are spheroids. Spheroidal dust particles have a factor 1.5–3 greater absorption cross section in the far-infrared than spherical grains of the same volume do. Mass estimates derived from submillimetre observations that ignore this effect are overestimated by the same amount. In the presence of a magnetic field, spheroids may be partly aligned and polarise light. We find that polarisation spectra help to determine the upper particle radius of the otherwise rather unconstrained dust size distribution. Stochastically heated small grains of graphite, silicates, and polycyclic aromatic hydrocarbons (PAHs) are included.