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CONSPECTUS: While some exceptional properties are unique to graphene only (its signature Dirac-cone gapless dispersion, carrier mobility, record strength), other features are common to other two-dimensional materials. The broader family "beyond graphene" offers greater choices to be explored and tailored for various applications. Transition metal dichalcogenides (TMDCs), hexagonal boron nitride (h-BN), and 2D layers of pure elements, like phosphorus or boron, can complement or even surpass graphene in many ways and uses, ranging from electronics and optoelectronics to catalysis and energy storage. Their availability greatly relies on chemical vapor deposition growth of large samples, which are highly polycrystalline and include interfaces such as edges, heterostructures, and grain boundaries, as well as dislocations and point defects. These imperfections do not always degrade the material properties, but they often bring new physics and even useful functionality. It turns particularly interesting in combination with the sheer openness of all 2D sheets, fully exposed to the environment, which, as we show herein, can change and tune the defect structures and consequently all their qualities, from electronic levels, conductivity, magnetism, and optics to structural mobility of dislocations and catalytic activities. In this Account, we review our progress in understanding of various defects. We begin by expressing the energy of an arbitrary graphene edge analytically, so that the environment is regarded by "chemical phase shift". This has profound implications for graphene and carbon nanotube growth. Generalization of this equation to heteroelemental BN gives a method to determine the energy for arbitrary edges of BN, depending on the partial chemical potentials. This facilitates the tuning of the morphology and electronic and magnetic properties of pure BN or hybrid BN|C systems. Applying a similar method to three-atomic-layer TMDCs reveals more diverse edge structures for thermodynamically stable flakes. Moreover, CVD samples show new types of edge reconstruction, providing insight into the nonequilibrium growth process. Combining dislocation theory with first-principles computations, we could predict the dislocation cores for BN and TMDC and reveal their variable chemical makeup. This lays the foundation for the unique sensitivity to ambient conditions. For example, partial occupation of the defect states for dislocations in TMDCs renders them intrinsically magnetic. The exchange coupling between electrons from neighboring dislocations in grain boundaries further makes them half-metallic, which may find its applications in spintronics. Finally, brief discussion of monoelemental 2D-layer phosphorus and especially the structures and growth routes of 2D boron shows how theoretical assessment can help the quest for new synthetic routes.