  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.
