The usefulness of a number of new stereological principles for unbiased estimation of particle number and sizes and sampling of particles is illustrated together with a novel principle for unbiased estimation of anisotropic surfaces. The examples include descriptions of estimators of neurone and synapse number and sizes, synapse gradients, neurone point patterns in three-dimensional space, capillary surface area, and perikarya volumes. A major advantage of the methods is the possibility to carry out the estimation procedures in specified, well-characterized regions or layers of the brain. Some general statistical and stereological problems are briefly discussed.