Genes containing the SET domain can catalyse histone lysine methylation, which in turn has the potential to cause changes to chromatin structure and regulation of the transcription of genes involved in diverse physiological and developmental processes. However, the functions of SET domain-containing (StSET) genes in potato still need to be studied. The objectives of our study can be summarized as in silico analysis to (i) identify StSET genes in the potato genome, (ii) systematically analyse gene structure, chromosomal distribution, gene duplication events, promoter sequences, and protein domains, (iii) perform phylogenetic analyses, (iv) compare the SET domain-containing genes of potato with other plant species with respect to protein domains and orthologous relationships, (v) analyse tissue-specific expression, and (vi) study the expression of StSET genes in response to drought and heat stresses. In this study, we identified 57 StSET genes in the potato genome, and the genes were physically mapped onto eleven chromosomes. The phylogenetic analysis grouped these StSET genes into six clades. We found that tandem duplication through sub-functionalisation has contributed only marginally to the expansion of the StSET gene family. The protein domain TDBD (PFAM ID: PF16135) was detected in StSET genes of potato while it was absent in all other previously studied species. This study described three pollen-specific StSET genes in the potato genome. Expression analysis of four StSET genes under heat and drought in three potato clones revealed that these genes might have non-overlapping roles under different abiotic stress conditions and durations. The present study provides a comprehensive analysis of StSET genes in potatoes, and it serves as a basis for further functional characterisation of StSET genes towards understanding their underpinning biological mechanisms in conferring stress tolerance.