Switchgrass and Reed Canarygrass are perennial forage crops that are being targeted for biofuels. We developed linkage and association mapping populations to learn more about the underlying genomic and phenotypic variation in these species. These populations were planted in New York and Wisconsin, where wide variation in numerous traits, e.g., leaf length and leaf width, was observed. Additionally, instability in chromosome number in switchgrass was noted, with tetraploids, hexaploids, octoploids, and aneuploids present in our populations. Genotyping by sequencing (GBS) was used to identify more than ten thousand SNPs in both species, providing unprecedented insight into their genomes. This work focuses on statistical models that use these SNPs for quick and accurate identification of genomic regions of interest, as well as favorable lines for use in breeding programs. The challenges that arose during the development of these models, such as the accommodation of varying ploidy levels into the analysis and the handling of missing data, are presented and addressed. Implementation of these models in genomic selection and genome-wide association studies has the potential to reduce standard breeding cycles of these perennial grass species from five or more years to one or two years.