Selection of functional traits is a challenge for researchers, but an increasingly necessary objective due to the growing concern regarding animal welfare and overcoming the problems of reducing antibiotic use in rabbit production without undermining the animals' productivity. The aim of this review is to discuss the genetic control of resistance to diseases, longevity and variability of birth weight within a litter, or litter size variability at birth within doe, and describing the selection programmes and the first results from a multi-omics analysis of resistance/susceptibility to diseases. The heritability is around 0.13 for longevity, 0.01 for uniformity in birth weight, 0.09 for litter size variability and around 0.11 for disease resistance. Genetic correlations between functional traits and production traits are mostly no different from zero, or are moderately favourable in some cases. Six selection programmes developed in three countries are reviewed. Line foundation with high pressure for selection or divergent selection experiments are different methodologies used, and favourable responses to selection have been obtained. Genomics studies have revealed associations in regions related to immune system functionality and stress in lines selected for litter size variability. Knowledge of gut microbiota role on the rabbit's immune response is very limited. A multi-omics approach can help to know microbial mechanisms on regulation immunity genes of the host.