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The electronic structure and physical properties of the pnictide compoundfamilies $RE$OFeAs ($RE$ = La, Ce, Pr, Nd, Sm), $A$Fe$_{2}$As$_{2}$ ($A$ = Ca,Sr, Ba, Eu), LiFeAs and FeSe are quite similar. Here, we focus on the membersof the $A$Fe$_{2}$As$_{2}$ family whose sample composition, quality and singlecrystal growth are better controllable compared to the other systems. Usingfirst principles band structure calculations we focus on understanding therelationship between the crystal structure, charge doping and magnetism in$A$Fe$_{2}$As$_{2}$ systems. We will elaborate on the tetragonal toorthorhombic structural distortion along with the associated magnetic order andanisotropy, influence of doping on the $A$ site as well as on the Fe site, andthe changes in the electronic structure as a function of pressure.Experimentally, we investigate the substitution of Fe inSrFe$_{2-x}TM_{x}$As$_{2}$ by other 3$d$ transition metals, $TM$ = Mn, Co, Ni.In contrast to a partial substitution of Fe by Co or Ni (electron doping) acorresponding Mn partial substitution does not lead to the supression of theantiferromagnetic order or the appearance of superconductivity. Most calculatedproperties agree well with the measured properties, but several of them aresensitive to the As $z$ position. For a microscopic understanding of theelectronic structure of this new family of superconductors this structuralfeature related to the Fe-As interplay is crucial, but its correct ab initiotreatment still remains an open question.

AFe2As2 (A = Ca, Sr, Ba, Eu) and SrFe_(2-x)TM_(x)As2 (TM = Mn, Co, Ni): crystal structure, charge doping, magnetism and superconductivity