Grain boundary complexions (phase-like interfacial structures) have been a major new area of exciting research. Analogous distinct structural states should also be possible at other types of defects such as dislocations, with recent experimental evidence of such features emerging from studies of Fe-Mn. In this work, we use atomistic modeling to study segregation and linear complexion formation along edge dislocations in both body-centered cubic and face-centered cubic metallic alloys. The local stresses associated with the dislocation can drive preferential segregation and local phase transformations, usually in the form of arrays of nanoscale precipitates. In Fe-Ni, we find that these precipitates are a combination of metastable B2-FeNi and stable L10-FeNi phases. For face-centered cubic metals, similar stress-driven segregation can occur but certain systems can also demonstrate segregation along the stacking fault between dissociated partial dislocations. For example, Cu-Zr can sustain a planar structure along the stacking fault that is reminiscent of the (111) plane of Cu5Zr. For all of these alloys, we map out composition and temperature space to formulate “linear complexion phase diagrams” that will serve to guide future processing studies. Finally, we explore how these linear complexions affect the movement of dislocations, with an eye toward manipulating strength and strain hardening.