The purpose of my dissertation is to understand the structural and magnetic properties of the newly discovered FeAs-based superconductors and the interconnection between superconductivity, antiferromagnetism, and structure. X-ray and neutron scattering techniques are powerful tools to directly observe the structure and magnetism in this system: High-resolution x-ray diffraction, x-ray resonant magnetic scattering, and neutron diffraction measurements have been used. I found that the structural and antiferromagnetic transitions are split in the parent BaFe₂As₂ compound with second-order structural transition temperature (T_S) higher than the first-order AFM transition temperature (T_N). Upon substitutions by Co and Rh, which are considered as electron doping, the structural and AFM transition temperatures are suppressed to lower temperature and split further. In contrast to the electron doping, in isoelectronic Ru substitution, the structural and AFM transitions are locked at the same temperature while in the hole doping case, the Mn substitution, the T_S and T_N occur at the same temperature up to approximately x = 0.102. Above x ≥ 0.11, the orthorhombic distortion is not observed while the AFM signal from the antiferromagnetic propagation vector Q_AFM of the “stripe” AFM structure remains. X-ray resonant magnetic scattering measurements at the Fe K edge add another example of resonance enhancement at the K edge of 3d element (in this case Fe) and definitely show that no incommensurate magnetic ordering exists in ≤ 5.4% Co substituted BaFe₂As₂ compounds. Neutron diffraction measurements show that the commensurate-to-incommensurate transition occurs in ≥ 5.6% Co substitution, ≥ 3.5% Ni substitution, but not in any level of Cu substitution. I show that simple electron counting based on rigid-band concepts is invalid. These results suggest that substitutional impurity effects in the Fe plane play a significant role in controlling magnetism and the appearance of superconductivity, with Cu distinguished by enhanced impurity scattering and split-band behavior.