Polyploidy has long been considered a major force in plant evolution. G. Ledyard Stebbins, Jr., an architect of the Modern Synthesis, elegantly addressed a broad range of topics, from genes to chromosomes to deep phylogeny, but some of his most lasting insights came in the study of polyploidy. Here, we review the immense impact of his work on polyploidy over more than 60 years, from his entrance into this fledgling field in the 1920s until the end of his career. Stebbins and his contemporaries developed a model of polyploid evolution that persisted for nearly half a century. As new perspectives emerged in the 1980s and new genetic tools for addressing key aspects of polyploidy have become available, a new paradigm of polyploidy has replaced much of the Stebbinsian framework. We review that paradigm shift and emphasize those areas in which the ideas of Stebbins continue to propel the field forward, as well as those areas in which the field was held back; we also note new directions that plant geneticists and evolutionists are now exploring in polyploidy research. Perhaps the most important conclusion from recent and ongoing studies of polyploidy is that, following Levin and others, polyploidy may propel a population into a new adaptive sphere given the myriad changes that accompany genome doubling.