This review provides a perspective on recent developments and their implications for our understanding of novel quantum phenomena in the physics of two-dimensional organic solids. We concentrate on the phase transitions and collective response in the charge sector, the importance of coupling of electronic and lattice degrees of freedom and stress an intriguing role of disorder. After a brief introduction to low-dimensional organic solids and their crystallographic structures, we focus on the dimensionality and interactions and emergent quantum phenomena. Important topics of current research in organic matter with sizeable electronic correlations are Mott metal-insulator phase transitions, charge order and ferroelectricity. Highly frustrated two-dimensional systems are established model compounds for studying the quantum spin liquid state and the competition with magnetic long-range order. There are also unique examples of quantum disordered state of magnetic and electric dipoles. Representative experimental results are complemented by current theoretical approaches.
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