Dissolved organic matter (DOM) is ubiquitous in aquatic environments where it interacts with a variety of particles including carbonaceous materials (CMs). The complexity of both DOM and the CMs makes DOM–CM interactions difficult to predict. In this study we have identified the preferential sorption of specific DOM fractions as being dependent on their aromaticity and molecular weight, as well as on the surface properties of the CMs. This was achieved by conducting sorption batch experiments with three types of DOM (humic acid, Suwannee River natural organic matter, and a compost extract) and three types of CMs (graphite, carbon nanotubes, and biochar) with different geometries and surface complexities. The non-adsorbed DOM fraction was analyzed by size exclusion chromatography and preferentially sorbed molecular weight fractions were analyzed by UV/vis and fluorescence spectroscopy. All three sorbent types were found to preferentially sorb aromatic DOM fractions, but DOM fractionation depended on the particular combination of sorbent and sorbate characteristics. Single-walled carbon nanotubes only sorbed the smaller molecular weight fractions (<1 kDa). The sorption of smaller DOM fractions was not accompanied by a preference for less aromatic compounds, contrary to what was suggested in previous studies. While graphite preferentially sorbed the most aromatic DOM fraction (1–3 kDa), the structural heterogeneity of biochar resulted in reduced selectivity, sorbing all DOM > 1 kDa. The results explain the lack of correlation found in previous studies between the amount of aromatic carbon in a bulk DOM and its sorption coefficient. DOM sorption by CMs was generally controlled by DOM aromaticity but complex sorbent surfaces with high porosity, curvatures and functional groups strongly reduced the importance of aromaticity.