The nature of the thermoelectric materials Ag(1-x)Pb(m)SbTe(m+2) or LAST-m materials (LAST for Lead Antimony Silver Tellurium) with different m values at the atomic as well as nanoscale was studied with powder/single-crystal X-ray diffraction, electron diffraction, and high-resolution transmission electron microscopy. Powder diffraction patterns of different members (m = 0, 6, 12, 18, infinity) are consistent with pure phases crystallizing in the NaCl-structure-type (Fmm) and the proposition that the LAST family behaved as solid solutions between the PbTe and AgSbTe2 compounds. However, electron diffraction and high resolution transmission electron microscopy studies suggest the LAST phases are inhomogeneous at the nanoscale with at least two coexisting sets of well-defined phases. The minority phase which is richer in Ag and Sb is on the nanosized length scale, and it is endotaxially embedded in the majority phase which is poorer in Ag and Sb. Moreover, within each nanodomain we observe extensive long range ordering of Ag, Pb, and Sb atoms. The long range ordering can be confirmed by single crystal X-ray diffraction studies. Indeed, data collections of five different single crystals were successfully refined in space groups of lower symmetry than Fmm including P4/mmm and Rm. The results reported here provide experimental evidence for a conceptual basis that could be employed when designing high performance thermoelectric materials and dispel the decades long belief that the systems (AgSbTe2)(1-x)(PbTe)x are solid solutions.