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We discuss recent developments in the field of first-principles calculations addressing the structural and electronicproperties of two-dimensional (2D) materials. The focus of the first part of the talk will be on silicene, the Si analogueof graphene, which is of great present interest due to its compatibility with the established Si technology. In particular, theeffects of the substrate and strategies for achieving a quasi- freestanding configuration are addressed. Layered transition metaldichalcogenides have shown the potential to achieve 2D materials applying routes based on specific growth techniques orresembling the exfoliation of graphene from graphite. The talk will focus on prototypical monolayer MoS2 to obtain insight intothe influence of defects and substitutional doping on the material properties, for a wide range of transition metal dopants. Polarmonolayers will be studied with respect to both their structural stability and the consequences of strong spin-orbit coupling.Strain is one of the most efficient tools to engineer to properties of monolayer transition metal dichalcogenides, thoughunexpected effects can be encountered. As an example, huge valley drifts off the corners of the Brillouin zone (K points) will bedemonstrate for uniaxial strain, more than an order of magnitude larger than in graphene. In the context of the emerging fieldof valleytronics, the dependence of the valley polarization on the interplay between the spin-orbit coupling and the exchangeinteraction will be discussed.