At the outset of solid organ transplantation, genetic variation between donors and recipients was recognized as a major player in mechanisms such as allograft tolerance and rejection. Genome-wide association studies have been very successful in identifying novel variant-trait associations, but have been difficult to perform in the field of solid organ transplantation due to complex covariates, era effects, and poor statistical power for detecting donor-recipient interactions. To overcome a lack of statistical power, consortia such as the International Genetics and Translational Research in Transplantation Network have been established. Studies have focused on the consequences of genetic dissimilarities between donors and recipients and have reported associations between polymorphisms in candidate genes or their regulatory regions with transplantation outcomes. However, knowledge on the exact influence of genetic variation is limited due to a lack of comprehensive characterization and harmonization of recipients' or donors' phenotypes and validation using an experimental approach. Causal research in genetics has evolved from agnostic discovery in genome-wide association studies to functional annotation and clarification of underlying molecular mechanisms in translational studies. In this overview, we summarize how the recent advances and progresses in the field of genetics and genomics have improved the understanding of outcomes after solid organ transplantation.