Complexions are phase-like features that are in equilibrium only at material defects. Complexion theory has been used extensively to describe grain boundary structural transitions, but recent work has also extended this framework to describe similar transformations at dislocation cores. Here, we bring atomistic modeling techniques to bear on these problems, with a focus on understanding the thermodynamics behind the transitions and the resultant atomic structures. First, we provide a critical look at interatomic potential selection for simulating these phenomena. Next, we explore grain boundary complexions transitions in binary and ternary alloys, followed by extension to linear complexion transitions. Finally, we discuss the effect of these new structures on subsequent material response.