The genera Boechera (A. Löve et D. Löve) and Arabidopsis, the latter containing the model plant Arabidopsis thaliana, belong to the same clade within the Brassicaceae family. Boechera is the only among the more than 370 genera in the Brassicaceae where apomixis is well documented. Apomixis refers to the asexual reproduction through seed, and a better understanding of the underlying mechanisms has great potential for applications in agriculture. The Boechera genus currently includes 110 species (of which 38 are reported to be triploid and thus apomictic), which are distributed mostly in the North America. The apomictic lineages of Boechera occur at both the diploid and triploid level and show signs of a hybridogenic origin, resulting in a modification of their chromosome structure, as reflected by alloploidy, aneuploidy, substitutions of homeologous chromosomes, and the presence of aberrant chromosomes. In this review, we discuss the advantages of the Boechera genus to study apomixis, consider its modes of reproduction as well as the inheritance and possible mechanisms controlling apomixis. We also consider population genetic aspects and a possible role of hybridization at the origin of apomixis in Boechera. The molecular tools available to study Boechera, such as transformation techniques, laser capture microdissection, analysis of transcriptomes etc. are also discussed. We survey available genome assemblies of Boechera spp. and point out the challenges to assemble the highly heterozygous genomes of apomictic species. Due to these challenges, we argue for the application of an alternative reference-free method for the comparative analysis of such genomes, provide an overview of genomic sequencing data in the genus Boechera suitable for such analysis, and provide examples of its application.