Variation in the genetic environmental sensitivity (GES) of livestock can cause genotype by environment interactions (G×E). The impacts of G×E differs depending on whether genotypes express different sensitivities across or within environments. Across environments G×E is caused by macro-GES, while within environments G×E is caused by micro-GES. Estimation of GES is challenging especially in unbalanced datasets. The number of animals in each macro-environment and the degree of genetic connection across macro-environments both influence the estimation accuracy of genetic variance due to macro-GES. Meanwhile, it has been suggested that balanced datasets with relatively large sire family sizes are required to accurately estimate micro-GES of single recorded traits. The aim of this thesis was to assess the data structure requirements for estimation of macro and micro-GES in unbalanced data, evaluate the accuracy of modelling micro-GES on one trait in multi-trait models, estimate the relationship between health-related traits and micro-GES of production traits, examine the interaction between macro- and micro-GES, and estimate the magnitude of macro- and micro-GES in livestock. The data structure requirements for estimation of macro- and micro-GES in unbalanced data, was evaluated using a simulation study in Chapter 3. It was shown that the accuracies and bias of estimated variance components for simultaneous estimation of macro- and micro-GES using double hierarchical generalised linear models (DHGLMs) including a linear reaction norm depended primarily on average sire family size. Accurate and unbiased estimates variance components and EBVs of macro- and micro-GES could be obtained with a dataset with 500 sires with 20 offspring per sire on average. The impact of differences in the number of records on the accuracy of variance component estimation when analysing multiple traits of which one exhibit micro-GES was assessed in Chapter 5. The genetic correlations were found to be slightly overestimated when the true genetic correlations were 0.5. However, the models were accurately able to identify the presence of non-zero genetic correlations, showing that these models could provide useful information. The relationship between health-related traits and production traits were examined in Chapter 6 by estimating the genetic correlation between immune competence traits and mean performance and micro-GES of weaning weight, eye muscle area and rib and rump fat depth. It was shown that animals with high immune competence tended to also have high mean performance and micro-GES of rib and rump fat and low mean performance and micro-GES of weaning weight and eye muscle area. The interaction between macro- and micro-GES of body weight in two subpopulations of the same cross reared in Burkina Faso and France was assessed in Chapter 7. Micro-GES of body weight showed considerable macro-GES with both heterogeneity of heritabilities and reranking between the two subpopulations. The existence of macro-GES and micro-GES were found for yearling weight of Australian Angus beef cattle and body weight of purebred and crossbred broiler chicken. Furthermore, micro-GES was found in weaning weight, eye muscle area and rib and rump fat in Australian Angus beef cattle