The current state of the chemical functionalization of three types of single sheet 2D materials, namely, graphene, molybdenum disulfide (MoS2), and black phosphorus (BP) is summarized. Such 2D sheet polymers represent currently an emerging field at the interface of synthetic chemistry, physics, and materials science. Both covalent and non-covalent functionalization of sheet architectures allows for a systematic modification of their properties, i.e. an improvement of solubility and processability, the prevention of re-aggregation or a band gap tuning. Next to successful functionalization concepts also fundamental challenges are addressed. These include the insolubility and polydispersity of most 2D sheet polymers, the development of suitable characterization tools, the identification of effective binding strategies, the chemical activation of the usually rather unreactive basal planes for covalent addend binding, and the regioselectivity of plane addition reactions. Although a number of these questions remain elusive in this review, the first promising concepts to overcome such hurdles have been listed.
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