The overall dimensions of global species richness remain very imprecisely known and the manner in which this richness is distributed only sketchily understood. This lamentable state of affairs is largely due to an inadequate appreciation of the contributions made by the most speciose groups. The most reliable, practical and cost-effective means of documenting patterns and estimating species richness in these groups is the use of a piecemeal, step by step, approach, eschewing the use of first principles, empirical relationships that are not directly amenable to calibration, diversity indices and `short cuts' that take no account of the effects of scale. Instead, simple ratios of species richness from taxon to taxon, focal group to more inclusive group, site to site, sample to inventory, and across spatial scales provide a basis for extrapolation. Essential features of this approach are the calibration of ratios, ensuring that like is compared with like, and the fullest use of `hands on' knowledge of the groups in question and the settings in which they are found. The choice and use of focal groups for extrapolation to larger groups and the choice and use of sampling methods to obtain reliable sample data from which to extrapolate to site inventories are considered in some detail. The way that the interplay between patchy distributions, method of sampling and sample `dimensions' influences the reliability and precision of estimates is also discussed. The importance of appropriate rigour in assembling the species datasets that form the basis of estimates, including care in the choice and use of sampling regimes and accuracy in species recognition and sorting, is stressed. Although species richness patterns in terrestrial arthropods are used here as examples, the principle of employing simple ratios for extrapolation is also applicable to other speciose groups and other settings.