Polyploidy is a major speciation process in vascular plants, and is postulated to be particularly important in shaping the diversity of extant ferns. However, limitations in the availability of bi-parental markers for ferns have greatly limited phylogenetic investigation of polyploidy in this group. With a large number of allopolyploid species, the genus Botrychium is a classic example in ferns where recurrent polyploidy is postulated to have driven frequent speciation events. Here, we use PacBio sequencing and the PURC bioinformatics pipeline to capture all homeologous or allelic copies of four long (∼1kb) low-copy nuclear regions from a sample of 45 specimens (25 diploids and 20 polyploids) representing 37 Botrychium taxa, and three outgroups. This sample includes most currently recognized Botrychium species in Europe and North America, and the majority of our specimens were genotyped with co-dominant nuclear allozymes to ensure species identification. We analyzed the sequence data using maximum likelihood (ML) and Bayesian inference (BI) concatenated-data (“gene tree”) approaches to explore the relationships among Botrychium species. Finally, we estimated divergence times among Botrychium lineages and inferred the multi-labeled polyploid species tree showing the origins of the polyploid taxa, and their relationships to each other and to their diploid progenitors. We found strong support for the monophyly of the major lineages within Botrychium and identified most of the parental donors of the polyploids; these results largely corroborate earlier morphological and allozyme-based investigations. Each polyploid had at least two distinct homeologs, indicating that all sampled polyploids are likely allopolyploids (rather than autopolyploids). Our divergence-time analyses revealed that these allopolyploid lineages originated recently—within the last two million years—and thus that the genus has undergone a recent radiation, correlated with multiple independent allopolyploidizations across the phylogeny. Also, we found strong parental biases in the formation of allopolyploids, with individual diploid species participating multiple times as either the maternal or paternal donor (but not both). Finally, we discuss the role of polyploidy in the evolutionary history of Botrychium and the interspecific reproductive barriers possibly involved in these parental biases.