This thesis focused on the estimation of genetic parameters for novel functional traits in dairy and dual-propose cattle populations including heat stress responses, methane emissions, longitudinal body weights and respective growth curve parameters as well as electronically recorded behavior pattern. In this regard, quantitative-genetics and genomic modelling approaches were applied. Moreover, genetic architectures for body weight and behavior traits were inferred, i.e., via GWAS for direct-genetic as well as maternal-genetic effects, and ongoing pathway analyses to identify potential candidate genes and their functional annotations. Possible G×E were studied, considering simultaneously continuous time (e.g., aging) and environmental descriptors (e.g., THI). As a novelty, genetic (co)variance components were estimated via RRM on genetic and genomic herd scales, aiming on a deeper understanding of G×E. In the original research paper 1, we stochastically simulated longitudinal phenotypic cow records at five THI levels, as well as genotypes from the 2,000 cows, aiming on the evaluation of the effects of heritabilities, LD, maker density and the proportion of phenotypic records for extreme THI, on prediction accuracies in genomic RRM. As expected, prediction accuracies increased with increasing heritability, LD and SNP density. In order to improve accuracies of genomic predictions, it was imperative to consider a proportion of cows with phenotypic records in heat stress environments (i.e., THI larger than 75), when estimating genomic breeding values of remaining genotyped but not phenotyped cows. In all scenarios, prediction accuracies were larger when modelling the G matrix instead of the A matrix. The advantage of RRM considering genotyped cows and heat stress interactions with regard to prediction accuracies for test-day milk yield and SCS was confirmed in original research paper 2. Four RRM, i.e., RRM with or without genotyped cattle combined with or without G×E interaction terms, were evaluated using 5-fold cross-validations. The highest prediction accuracies for both traits were identified when applying genomic RRM, and modelling THI as an environmental descriptor. Such modelling superiority was stronger for milk yield than for SCS. For test-day milk yield, a quite large range in genetic correlation estimates for days in milk × THI combinations were identified, indicating GxE interactions. For test-day SCS, genetic correlations were more stable and throughout larger than 0.80. In conclusion, for traits showing sensitive responses to heat stress such as milk yield, it is imperative to include a heat stress indicator in genetic evaluation models, which also contributes to the improved identification of robust dairy cattle in harsh environments. Genetic parameters for test-day CH4, which were predicted through a deterministic approach as well as an approach combining deterministic equations and stochastic simulations, were estimated on a time scale via RRM in original research paper 3. The heritabilities for daily CH4 ranged from 0.15 to 0.37. Genetic correlations between CH4 from different prediction equations were larger than 0.90. Antagonistic genetic correlations in the range from 0.70 to 0.92 were estimated between CH4 and milk yield. Genetic correlations with other functional breeding goal traits were close to zero, but altered in the course of lactation. The simulated data basis for CH4 was used to determine the size of a cow calibration group for genomic selection. A calibration group including 2,581 cows with own measurements for CH4 (a heritability of 0.44 and an effective population size of 100) was competitive with conventional breeding strategies in terms of prediction accuracy. Genetic parameters and genetic architectures for body weight from different ages were studied in the original research papers 4 and 5, respectively. Body weight from birth to calving had moderate to high direct heritabilities. The maternal genetic component was detectable for body weights of calves in the period from birth to an age of 5 months, but later on, maternal genetic variances were close to zero. Body weights for calves and heifers were weakly correlated with production, female fertility and health traits in first parity cow. Genetic correlations between production and fertility traits with insemination body weight were stronger than with birth weight. Considering genomic data of genotyped cows, heritabilities as presented in the original research paper 5 verified the genetic parameter estimates (original research paper 4). Furthermore, in the original research paper 5, GWAS for birth weight, weaning weight and body weight at the first insemination date inferred significantly associated SNP and underlying potential candidate genes. With regard to GWAS for maternal-genetic effects, three SNP were significantly associated with birth weight according to the threshold based on 5% false discovery rate. No SNP significantly contributed to maternal-genetic effects on body weight recorded at weaning and at first insemination. Gene annotations identified 76 potential candidate genes for body weight, and these genes were involved in 12 biological processes. Hence, weight development is a very complex biological process, which is controlled by many genes with minor effects. Original research paper 6 focused on the estimation of genetic parameters and on prediction accuracies for growth curve parameters from three non-linear growth models, i.e., the Logistic, the Gompertz and the Richards functions, in combination with different kernel similarity matrices. Moderate heritabilities for growth curve parameters confirmed the pronounced genetic background for body weight with aging. Prediction accuracies for genomic growth curve parameters from different similarity matrices, including two genomic relationship matrices and three kernel matrices, combined with same non-linear functions, were very similar. In combination with all genomic relationship and kernel matrices, model superiority and largest prediction accuracies were observed when fitting the non-linear Richards function. Heritabilities for novel behavior traits, which were electronically recorded via ear tag sensors, ranged from 0.04 for rumination to 0.20 for feeding and high active. Differences in heritabilities and genetic variances indicate a diverse genetic background for different behavior traits. The underlying genetic mechanisms were unraveled through multi-breed GWAS in original research paper 7. According to a very relaxed threshold based on 20% false discovery rate, only five SNP were significantly associated with rumination, one SNP with feeding and one SNP with “not active”. The reason for the quite small number of significantly associated SNP with natural cattle behavior might be short-range LD when pooling breeds or limited conserved mutations across breeds. Mendelian randomization based on genomic variants (i.e., the instrumental variables) was used to infer causal inference between an exposure and an outcome. For example, the regression coefficients of rumination and feeding on milk yield were 0.10 kg/% and 0.12 kg/%, respectively, indicating their positive influences on dual-purpose cow productivity. Genomically, an improved welfare behavior of grazing cattle, i.e., a higher score for welfare indices, was significantly associated with increased fat and protein percentages. The original research paper 8 depicted possible G×E for production traits and SCS along phenotypic, quantitative-genetic and genomic herd descriptors. Hence, we provided the proof that genetic covariances and correlations between same traits from different herds strongly depend on genetic and genomic herd characteristics, such as inbreeding coefficients or LD within specific chromosomal segments. Apart from the herd variable “allele frequency for the SNP ARS-BFGL-NGS-4939 within the DGAT1 gene”, genetic correlations between milk yield at minimal and maximal levels for the other descriptors were always lower than 0.6, indicating environmental sensitivity. Especially for low heritability SCS, low genetic correlations were estimated when considering extreme herd classes according to LD of a genomic region on chromosome 6 at herd level, herd size, intra-herd percentage of non-EU sires, and the herd average for non-return rate. Alterations of estimated breeding values of sires in dependency of phenotypic, genetic and genomic herd structures suggest utilization of specific sires for specific herds, indicating further possibilities to optimize mating programs. Original research paper 9 addressed the importance of genotyped cows from a commercial herd perspective, including economic aspects and phenotype predictions. For different herd replacement strategies and a herd breeding goal aiming on antagonistically related production and functionality, genetic gain was maximized when focusing on large-scale female cattle genotyping. Especially selection response on the cow-dam pathway increased, through improved replacement and mating designs. From a literature review perspective, the original research paper 9 discussed further opportunities of cow training sets and commercial cow genotyping. Several studies and theoretical derivations highlighted the importance to including genotyped female cattle in training sets, because cow training sets avoid biased genomic predictions due to intensively pre-selected sires. Additionally, long-term genetic gain in novel functional traits is only possible when implementing the cow training sets. Detection of non-additive genetic effects as well as the control of inbreeding and genetic relationships (to avoid lethal defects) were further arguments to genotype cows in commercial herd. In conclusion, mainly based on studies using comprehensive datasets for genotyped cows recorded for novel traits, the habilitation thesis presented results for broad genetic mechanisms and identified potential candidate genes for various functional traits. Additionally, G×E were detected along novel continuous “environmental” gradients for both production and functional traits. These findings are important for future improvements of dairy cattle breeding programs, e.g., when expanding breeding goals with further functional trait categories (e.g., behavior traits), and simultaneously considering environmental sensitivity (e.g., heat stress response).