Progress in addressing critical epitaxial design issues associated with AlGaInP -based visible (red) vertical-cavity surface-emitting laser (VCSEL) diodes is reviewed, with emphasis on those issues that differentiate red VCSELs from conventional AlGaAs -based near-IR VCSELs. Key issues include epitaxial growth techniques for red VCSELs, the unique properties of AlGaInP alloys and heterostructures, design and growth of visible distributed Bragg reflectors, and integration of AlGaInP and AlGaAs hetero-structures into the hybrid VCSEL device structure. The performance characteristics of AlGaInP/AlGaAs red VCSEL diodes are overviewed in the context of the epitaxial design.