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Abstract The d1 layer metals TaS2, TaSe2, NbSe2, in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as ‘anomalous’. Our present electron-microscope studies indicate that this anomalous behaviour usually includes the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d1/5d1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of charge and spin-density waves. When they first appear, the CDW's in the 1T (and 4Hb) polytypes are incommensurate with the lattice. This condition produces a fair amount of gapping in the density of states at the Fermi level. For the simplest case of 1T-TaSe2, the room temperature superlattice is realized when this existing CDW rotates into an orientation for which it then becomes commensurate. At this first-order transition the Fermi surface energy gapping increases beyond that generated by the incommensurate CDW, as is clearly evident in the electromagnetic properties. For the trigonal prismatically coordinated polytypes, CDW formation is withheld to low temperatures, probably because of the more complex band structures. This CDW state (in the cases measured) would seem at once commensurate, even though the transition is, from a wide variety of experiments, apparently second order. A wide range of doped and intercalated materials have been used to substantiate the presence of CDW's in these compounds, and to clarify the effect that their occurrence has on the physical properties. The observations further demonstrate the distinctiveness of the transition metal dichalcogenide layer compounds, and of the group VA metals in particular.