This paper provides an overview of recent studies on the anisotropy of magnetostriction of functional iron-based alloys with the body-centered cubic (bcc) structure; these are potential ferromagnetic materials for use in actuators and sensors at ambient temperature. The magnetostrictive properties of these functional iron-based alloys (such as Fe–Ga, Fe–Al, and Fe–Ge alloys) are known to strongly depend on the crystallographic orientation. In these functional iron-based alloys, non-Joulian magnetostriction, in which volume is not conserved, was observed; generally, the Joulian magnetostriction in a volume is not altered by magnetic fields. As the magnetostrictive properties of these iron-based alloys are correlated to their elastic properties through the magnetoelastic effect, their elastic properties have also been investigated using single crystals of iron-based alloys. In the present paper, we discuss the characteristic features of the anisotropy of magnetostriction and inverse magnetostriction, which occur when magnetic fields and external stresses, respectively, are applied. In order to clarify the microscopic processes underlying the magnetostriction and inverse magnetostriction, the alterations in the magnetic domains by magnetic fields and external stresses were observed. The results revealed that the magnetic domain structure in the functional iron-based alloys is altered in a complex manner when applied with external fields. For example, it was demonstrated that unique motions of different types of Bloch domain walls are observed with the application of magnetic fields or external stresses along specific directions of single crystals of Fe–Ga alloys. The characteristic features of the motion of the domain walls are likely to correspond to the occurrence of magnetostriction and inverse magnetostriction, in which magnetic fluxes are induced during alternative vibration.