Theory revealed the nature of bonding and structure of several representatives of binary IIA–IVA and IIIA–IVA monolayers with novel chemical, physical, and topological properties based on reduced dimensionality. Unfortunately, experimental verification of these 2D materials has not been achieved. The hypercoordinate motifs with multicentered bondingMulticentered bonding and delocalized π electrons realized in these networks offer an extended platform in 2D materials chemistry, providing access to novel low-dimensional structures with innovative physicochemical properties. Density functional theory calculations and treatment of the exchange correlation energy within the generalized gradient approximation with suitable functionals yielded the binding energy and structural properties. The global minimumGlobal minimum structure search with particle swarm optimizationParticle-Swarm Optimization (PSO) using crystal structure analysis via the particle swarm optimization package identified the lowest energy configuration of the potential energy surface for several compounds. Of particular interest in these rule-breaking quasi-planar structures is the electron density distribution. The electron localization function and solid-state adaptive natural density partitioning methods allow notable insight into the type of bonding by elucidating the distribution of electrons. The critical points are the energetic stability given by a negative cohesive energyCohesive energy, the dynamic or kinetic stability requesting the absence of imaginary or negative frequencies, and the thermal stabilityThermal stability at elevated temperatures. Despite the enormous relevance of mechanical properties for the preparation and application of 2D materials, only linear properties such as Young’s moduli and Poisson’s ratiosPoisson´s ratio have been determined, with negative Poisson ratiosNegative poisson ratio (NPR) occurring for some compounds. The unique bonding types imply potential applications in various fields, such as electronics, optoelectronicsOptoelectronics, spintronicsSpintronics, photovoltaicsPhotovoltaics, mechanics, and sensoricsSensorics. Plots of the cohesive energyCohesive energy versus bond length and of the ultimate stiffnessStiffness and strength versus bond length allow insight into the fundamental structure–property relationships of these compounds with unconventional bonding behavior and astonishing good stability.