A far-infrared complete sample of southern galaxies with L(FIR)/L(B)0 greater than or similar to 3, for which optical, radio continuum and CO (J = 1-->0) line observations are available, is discussed. The far-infrared luminosities of these so-called extreme IRAS galaxies range from 10(9) to 10(12)L.. These galaxies show on average more active star formation than the galaxies in the IRAS Bright Galaxy Survey and the optical Revised Shapley-Ames Catalog. Dust masses derived from the IRAS data give gas-to-dust mass ratios close to the canonical Galactic value only if a two-component dust model is used with warm dust (60 K) associated with star forming regions and cool dust (18 K) associated with the general interstellar medium. The optical colours of the galaxies are completely dominated by the emission from the older population of stars already existing before the starburst. The large spread in the optical colours is due to extinction by dust in the disk, which, however, is not correlated with the extinction found towards the starforming regions determined from the Halpha/Hbeta line ratios. About 25% of the galaxies in the sample show LINER-type spectra which originate from vigorous nuclear star formation rather than from an active nucleus. Only about 8% of the galaxies in the sample are ''classical'' Seyferts. The sample can almost be divided into three distinct subgroups: dwarf galaxies (M(B) less-than-or-equal-to 19 mag), barred spirals and interacting systems, in order of increasing average L(FIR)/L(B)0 ratios. The dwarf galaxies show extended star forming regions, which can cover as much as half of the optical disk, while in the barred spirals and the interacting systems the star forming regions are confined to the centres, with typical diameters of approximately 1 and approximately 3 kpc, respectively. The striking absence of normal non-barred spiral galaxies in our sample implies that star formation in spiral arms is not an efficient way to power the far-infrared emission.