Intermetallic compounds have been investigated over several decades for their interesting structural and physical properties, including magnetism and superconductivity. Among these, metal pnictides and chalcogenides of transition metals show diversity of bonding ranging from appreciable covalency to metal–metal bonds, which makes these compounds highly complex. ZrCuSiAs and ThCr2Si2 are of interest, because they provide an opportunity to design interesting intermetallics with tetrahedral layers exhibiting quasi-two-dimensional behavior. However, these metal pnictides and chalcogenides were not well known for their superconducting properties. The recent discovery of superconductivity at 26 K in a ZrCuSiAs-related structure (LaO/FFeAs) created huge excitement in the field of metal pnictide and chalcogenide superconductors. The role of the FeX4 tetrahedra is significant for superconductivity. Distortion of the tetrahedra lowers the superconducting transition temperature (Tc) in these Fe-based superconductors. This article discusses the structural aspects of various new (2008–2011) families of Fe-based superconductors containing FeX4 tetrahedra (X = As and Se) that act as charge carrier layers in these superconductors.