The science of stereology has undergone a revolution over the past decade with the introduction of design-based (assumption- or model-free) methods which are highly efficient and generally unbiased. No other morphometric approach currently offers these twin benefits. Stereology is ideal for extrapolating 3-D structural quantities (real volumes, surface areas, lengths and numbers) from simple counts made on 2-D slice images. The images may take various forms (e.g. physical or optical sections, MRI slices, CT scans) but they must be sampled so as to be random in orientation and/or position if valid estimates are to be made. All the recent developments in stereology are applicable to problems in neuromorphometry. This review provides an account of major developments and the state of the art, emphasizes the importance of properly randomized sampling and identifies some applications to neural structure at different levels of organization. These include the counting and sizing of synapses, neurites, cells and whole brains.