Calcium-dependent protein kinases (CDPKs or CPKs), unique to plants and some protists, are involved in growth and developmental processes as well as in defence against diverse environmental stresses. CDPKs are encoded by multi-gene families. Despite extensive studies of the CDPKs in many species, information about the evolutionary history and expression patterns of the CDPK family in the staple crop potato (Solanum tuberosum) remains poorly known. In this study, we performed bioinformatics analysis of the potato whole genome sequence and identified 23 potential CDPK genes. These genes are located in 11, of 12, potato chromosomes. Based on the phylogenetic tree and gene structures, the CDPKs were divided into four subfamilies. To determine their expression, reverse transcription quantitative polymerase chain reaction (RT-qPCR) analysis was carried out for the CDPK genes in different organs of potato such as young and mature leaves, stems, young shoots, roots, stolons, swollen stolons, flowers and tubers. The CDPKs were expressed in all the organs analysed, but their expression patterns varied greatly. The expression of some CDPKs was strongly organ specific, for example StCPK13 and StCPK18 was found only/mostly in flowers. In Solanum genotypes differing in resistance to Phytophthora infestans, the expression and activity of CDPKs increased in response to a P. infestans elicitor with different kinetics and intensity. The expression levels and activity of the CDPKs correlated positively with the level of the resistance. Our results support earlier suggestion that CDPKs are involved in potato organ development and defence against stresses. We provide new information about the CDPK gene family in the potato and a perspective on its evolutionary history and biological roles of the individual kinases.