Lattice-mismatched relaxed graded composition layers in the SiGe/Si, InGaAs/GaAs, and InGaP/GaP systems have recently been created with unprecedented high quality due to advances in understanding the impact of epitaxial growth conditions. The key process–property correlation is the impact of growth conditions on dislocation dynamics. In particular, the SiGe/Si system has recently been well explored experimentally, allowing the dislocation dynamic model to be tested. We show that the dislocation dynamics model is in general applicable to graded layers in any material system as long as dislocation flow is not impeded. In the SiGe/Si, InGaAs/GaAs, and InGaP/GaP systems, with moderately dislocated graded layers, these mechanisms can be absent under appropriate growth conditions. However, in all systems, threading dislocation impediments eventually occur under continued deformation through continued grading. The mechanism in SiGe/Si is related to the impediment of dislocation flow from the surface morphology and strain-fields from misfit dislocations. In the III–V systems, we observe that a planar defect, referred to here as branch defects, can form under a wide range of growth conditions, and these defects will lead to inhibited dislocation flow. The quantitative nature of these effects can be empirically modeled with the same dislocation dynamic model by incorporating a composition-dependent change in the effective strain experienced by threading dislocations during grading-induced deformation.