After a brief introductory discussion of Brillouin zones, Fermi surfaces and the free-electron approximation, the present state of knowledge of the details of the topology and dimensions of the Fermi surfaces of the s-block and p-block metals and semi-metals is reviewed in detail. These materials include elements from groups IA, IIA, IIIB, IVB and VB of the periodic table. It is shown that the free-electron model gives a good first approximation to the description of the Fermi surfaces of many of these elements; the implication of this fact in the use of the pseudopotential method in describing the electronic properties of these materials is briefly discussed. An indication is given of gaps in the present knowledge of the geometry of the Fermi surfaces of these elements and suggestions are made for future experimental and theoretical work. © 1969, Taylor & Francis Group, LLC. All rights reserved.