Modulated structures are commonly found in transition-metal chalcogenides with compositions between MX 4 and M 3 X 4 . Their origin is in the low-dimensional character of these compounds, which supports phenomena like charge density waves (CDW). These can be further stabilized at surfaces, where the bulk dimensionality is additionally reduced. Modern surface methods, combined with calculations of the electronic properties, can give a new insight into such phenomena.Two weak incommensurate modes, superimposed onto the main breathing mode, were discovered during the initial TEM studies of Nb 1-x Ta x Te 4 . They were detected at the NbTe 4 side of the phase diagram as weak and diffuse satellites in overexposed electron diffraction patterns [1]. Although a bulk phenomenon, these modes were for the first time successfully resolved by STM [2]. This was possible due to the preferential cleavage of the NbTe 4 crystals, which exposed complete tetragonal anti-prismatic columns. The weak transversal modes were observed as a surface phenomenon, superimposed onto the much stronger breathing mode (Fig.1).The observed sliding of two apparently independent low-temperature CDWs in NbSe 3 was recently explained on basis of a new model [3], which took into account statistically distributed nanodomains of both CDW modes. The results of earlier low-temperature STM [4] and satellite dark field TEM studies [5] were shown to be in a good accord with the model. It was further shown that sub-monolayer gold deposits on the NbSe 3 van der Waals surface exhibit poorly correlated modulated regions, whose periodicities are comparable to those of the two CDWs in pure NbSe 3 . In another trichalcogenide, ZrTe 3 , a surface compositional modulation [6] was shown to be a result of ordered, surplus tellurium atoms, which occupied the interstitial positions on the (001) ZrTe 3 surface. Calculations within the extended Hückel tight binding (EHTB) approximation show that these tellurium atoms also account for the relatively high metallic conductivity of this compound.CDW domains of two orientational variants were detected at the edges of disk-like surface defects in NbSe 2 , which was an indication that the deformed regions of the Se-Nb-Se sandwiches assumed an octahedral rather than trigonal-prismatic coordination [7]. It was further shown that surface domain boundaries between orientational variants in the monoclinic NbTe 2 were often strongly modulated (Fig.2) with periodicities identical to those of the adjacent domains [8]. In contrast to the modulation in NbSe 2 , the NbTe 2 modulation was interpreted on basis of a misfit between the domain boundaries across the van der Waals gaps. Finally, the Nb 3 X 4 (X = S, Se, Te) compounds, characterized by large hexagonal tunnels [9], were studied by means of TEM and STM. From the three compounds forming the family only Nb 3 Te 4 shows bulk conductivity anomalies at 95 K, which were attributed to a CDW with a modulation vector q = ±(1/3a* + 1/3b* + 3/7c*). Intercalation with indium and thallium raises th...