Invited review: Novel methods and perspectives for modulating the rumen microbiome through selective breeding as a means to improve complex traits: Implications for methane emissions in cattle

•Rumen microbiome composition is partially controlled by the host genomics, both at the taxonomic and microbial function levels, with heritabilities ranging between 0.10 and 0.40.•Analyzing the microbiome poses some challenges that need to be carefully considered: large complexity, compositionality and lack of standardized bioinformatic procedures.•Rumen microbiome plays an important role influencing the phenotypic variability of feed digestion related traits, including methane, and it may need to be properly accounted for in the statistical genetic models.•Microbiota information may be included in the breeding programs, although specific strategies need to be defined in the future.