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Two-dimensional graphene-like silicon carbide (2d-SiC) has emerged as an intriguing new class of layered nanostructure. Using density functional theory, key electronic and optical properties of 2d-SiC nanosheets, in particular, of mono- and bilayer 2d-SiC, are investigated. The properties of these nanosheets are found to be highly dependent on their physical thickness and geometric configuration. Multilayer 2d-SiC exhibits an indirect bandgap. We find that monolayer 2d-SiC, on the other hand, has a direct bandgap (∼2.5 eV) that can be tuned through in-plane strain. We also show that the optical conductivity of multilayer 2d-SiC is sensitive to the interlayer spacing. The results suggest that unlike graphene, silicene and even multilayer 2d-SiC, monolayer 2d-SiC could be a good candidate for optoelectronic devices such as light-emitting diodes.