In recent years, marker-assisted selection (MAS) has been intensively used to increase the efficiency of potato breeding. Large-scale studies of the potato genome and genes exploiting next-generation sequence (NGS) approaches are required for the widespread application of MAS as well as genomic selection and genomic editing (the newest approach for creating potato plants with the desired properties). In this review, the trends in potato NGS-based research are overviewed and the related Internet resources are systematized. Special attention is given to the peculiarities of the models and approaches used in genetic studies of potato, taking into account the complex organization of its genome and a high level of heterozygosity. In genetic studies diploids, including diploid potato species, artificially obtained heterozygous dihaploids, and homozygous double monoploids, are often used. The availability of artificially created diploid forms played a fundamental role in sequencing the potato genome, which was completed in 2011. The activities of the Potato Genome Sequencing Consortium (PGSC) included not only constructing genome libraries, sequencing, assembling and annotating the genome but also genome sequence-based investigations uncovering the features of the potato genome’s evolution, SNP identification, analysis of genes and gene networks regulating resistance to phytopathogens, and the technological characteristics. An important outcome of genome sequencing was the identification of more than 8000 SNPs and approbation of the genotyping-by-sequencing (GBS) method on potato, which is the basis for the genomic selection of potato and for the discovery of economically important genes using genome wide association studies (GWAS). Optimizing the existing bioinformatic tools to support these studies, taking into account the peculiarities of the potato genome’s organization, are carried out. This review analyzes the databases containing the results of sequencing the potato genome and transcriptome, as well as the accompanying resources. This information should prove useful while planning comparative assays of the potato transcriptome or applying DNA-markers. The sequencing of the genome, as well as the transcriptomes and microRNomes, of the cultivated potato and its wild relatives, on one hand, is of fundamental interest, assisting in detecting the features of the genome’s evolution, ontogenetic development, and mechanisms of various environmental stress responses. On the other hand, it is the basis for a wide range of practical applications for developing effective genomic and gene-specific markers and marker-assisted breeding of new potato cultivars with the desired properties.