During the last decade genomic selection has revolutionized the dairy cattle breeding programs. For example, the Nordic dairy cows (Denmark, Sweden, Finland) born in 2018 were >90% sired by young genomic tested bulls. The average age of sires for Red Dairy Cattle (RDC) cows born 2018 was 3.1. While before the key driver of genetic progress was the selection of progeny tested sires, it is now the young sire preselection. This leads into difficulties in estimation of genetic progress by the traditional genetic evaluations. The only long-term solution is to include the genomic information into national animal model evaluations. Although means for this; that is, single-step evaluation models, have been available since 2010, they have not been yet implemented in large-scale national dairy cattle evaluations. At the first, single-step evaluations were hindered by computational cost. This has been largely solved by sparse presentations of G⁻¹ (genomic relationship) and A₂₂⁻¹ in single-step GTBLUP, or in APY approach, or using single-step marker models. In our test runs with 10.3 M beef cows and 1.5 M genotypes, each ssGTBLUP iteration of 6-trait calving difficulty model took roughly 4 times longer than pedigree animal model iteration. Concurrently with algorithm development, the computing resources have evolved both in availability of RAM and CPUs. The problems actively studied now are the same for the both single-step approaches (GBLUP and marker models). In both the convergence in iterative solving seems to get worse with increasing number of genotypes. Problems are clearer with low heritability traits, and in multi-trait models with high genetic correlations among traits. Additionally, it seems that they interact with unbalancedness of pedigrees and diverse genetic groups. Standard iteration approach is preconditioned conjugate gradient, in which the convergence has been improved with better preconditioning matrices. Another difficulty to be considered is the inflation in genomic predictions for selection candidates. The genomic models seem to overvalue the genomic relationship (or SNP) information. The problem is usually smaller in single-step evaluations than in multi-step evaluations but is more difficult to cover by “tune-up” parameters.