Two-dimensional materials (2DMs) have attracted tremendous research interest over the last two decades. Their unique optical, electronic, thermal, and mechanical properties make 2DMs key building blocks for the fabrication of novel complementary metal-oxide-semiconductor (CMOS) and beyond-CMOS devices. Major advances in device functionality and performance have been made by the covalent or noncovalent functionalization of 2DMs with molecules: while the molecular coating of metal electrodes and dielectrics allows for more efficient charge injection and transport through the 2DMs, the combination of dynamic molecular systems, capable to respond to external stimuli, with 2DMs makes it possible to generate hybrid systems possessing new properties by realizing stimuli-responsive functional devices and thereby enabling functional diversification in More-than-Moore technologies. In this review, we first introduce emerging 2DMs, various classes of (macro)molecules, and molecular switches and discuss their relevant properties. We then turn to 2DM/molecule hybrid systems and the various physical and chemical strategies used to synthesize them. Next, we discuss the use of molecules and assemblies thereof to boost the performance of 2D transistors for CMOS applications and to impart diverse functionalities in beyond-CMOS devices. Finally, we present the challenges, opportunities, and long-term perspectives in this technologically promising field.