One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated with the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This perspective surveys these recent advances and discusses the novel research opportunities that arise from them.