Genetic evaluations for sport horses are performed by many Northern European studbooks, and estimated breeding values - which aid the selection of horses for breeding progeny with good competing ability - are routinely published. Either competition data or young horse evaluation data, or frequently a combination of both is used. Genetic evaluations are not yet performed in GB, and to date the only research conducted has been for the sport of eventing. The aims of this thesis were to: i) perform genetic evaluations for performance in dressage, including considering the effect of breed, ii) perform genetic evaluations for eventing, extending previous work, by using and comparing different methods of producing large (co)variance matrices and using a larger dataset, iii) characterise for the first time data recorded in the recently established young horse evaluation scheme, and if possible perform genetic evaluations and iv) investigate the suitability of international performance data for genetic evaluations for showjumping. Competition data was obtained from the national competition bodies and young horse evaluation data from the British Equestrian Federation. Pedigree was sourced from both. Appropriate mixed effects models were developed; animal models were used where pedigree data was sufficient, and sire models otherwise. Variance components were estimated using residual maximum likelihood and estimated breeding values were predicted using best linear unbiased prediction. Eventing comprises 3 disciplines, each with 4 grades i.e. 12 traits. For the evaluation, multivariate variance component analysis was performed, using and comparing three different methods of estimating the large 12 by 12 (co)variance matrices required for breeding value prediction. Significant, but low, heritabilities were found for dressage (0.07 – 0.09) and showjumping (0.09 – 0.16), and in the lower grades of cross-country (0.01), indicating that genetic progress for competition performance can be made by selection, particularly in showjumping. Genetic correlations within dressage and showjumping were high whereas those across disciplines were generally low and only significant for some of the lower grades, particularly between dressage and showjumping. Twelve breeding values were predicted for each horse. The methods based on combining covariance matrices from bivariate analyses were found to be the most reliable. In the dressage evaluations, significant heritabilites of 0.15 without accounting for breed effects and 0.11 when accounting for breed were found. Breed had a significant effect on competition performance, with warmbloods performing better than other breed groups. The model including breed was found to be the most appropriate for genetic evaluations in GB, although not currently implementable in practice due to limited recording of the breed identifier. In the young horse scheme, owners select which discipline (dressage, showjumping or eventing) their horse will enter. Traits are then recorded within the intended discipline. For the analyses, a genetic correlation of 1.0 was assumed between the same trait recorded in different disciplines. Significant, moderate, heritabilites were found for all five traits – veterinary (0.25), type and temperament (0.42), athleticism (0.20), conformation (0.29) and correctness of paces (0.30). The young horse scheme appears to be successful in establishment and uptake. Evaluations were performed for showjumping using international competition data. The small size of the dataset (approximately 6239 records on 479 horses) and large degree of selection limited the study. A larger dataset, including national data, needs to be made available to perform more accurate evaluations. However, an upper limit on the heritability was estimated to be 0.09 (standard error 0.012). This study explored the use of competition and young horse data for genetic evaluations. The eventing evaluations were the most reliable, and breeding values have been estimated which are ready for publication. However, there are certain limitations to all the competition data sources; there was selection in the data available for dressage and showjumping that biases the analyses. In addition, there were general limitations in the recording of competing horses, and in pedigree recording that limit the accuracy of the analysis. The young horse data represents a very valuable data source for genetic evaluations, although the scheme is still in its early stages. Ultimately, the most appropriate genetic evaluations will likely use a combination of young horse data and adult competition data. Further work can now perform multi-trait genetic evaluations using multiple data sources, such as combining young horse and competition data, or multiple competition disciplines.