Onset of genomic selection changed the focus of animal evaluation experts into estimation of genomic breeding values (GEBV). This was because of enormous potential of genomic information, but also because of similar intellectual challenges in methodologies. Still, also GEBV rely on phenotypes as a source of information. The GEBVs and the ordinary estimated breeding values (EBV) have the same need of well-defined models to attain accurate and unbiased results. Milk and component yield EBVs can illustrate the value of accuracy. Although EBV_protein or EBV_fat can be used as a indirect estimates of EBV_milk (correlations to milk EBV 0.91 and 0.79), the GEBV_milk trained on protein (fat) gave validation reliability of 0.27 (0.10), while the training on milk gave R² = 0.45. In this presentation we discuss particulars of breeding value estimation models and approaches for estimation of variance components (VC). The examples used are the joint Nordic test day model and the multiple trait-across country (MACE) model. The Nordic test day model is used to evaluate bulls and cows in Finland, Sweden and Denmark for 4 breeds: Holstein, Red Dairy Cattle, Jersey and FinnCattle. The challenges are the varying production conditions and admixed populations. The model is a multilactation, multitrait (milk, protein, fat) random regression. In every evaluation run the heterogeneity of variance is estimated for each trait and herd-year. During the implementation, VC for 1,827 parameters were estimated for each country and breed combination. Estimation was done using Monte Carlo REML and EM-algorithm. Most genomic evaluations rely on genotype exchange and MACE results for training. Accuracy of MACE depends on the assumed correlations across countries. Currently Interbull estimates correlations among breeding values of bulls from 31 countries, 6 breeds and 40 traits. The largest single VC estimation is for the Holstein production traits involving all countries. The challenges are computing, and the lack of genetic ties among smaller countries. Current estimation is by subsets of countries, but another alternative is to use MC REML and all countries simultaneously.