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Recent progress has been made in the understanding of strain accommodation and relief in lattice-mismatched semiconductor heterostructures. Specific recent advances include the following: improved understanding and modeling of competing strain relaxation mechanisms; quantification of misfit dislocation nucleation processes; improved modeling of critical epilayer thickness for misfit dislocation introduction; improved understanding of misfit dislocation nucleation mechanisms; new experimental techniques for in-situ observation of strain relaxation; new techniques for reduction of strain-relieving dislocations; and new calculations of dislocation electronic structure.