Potato (Solanum tuberosum L.) is often considered as a drought sensitive crop and its sustainable production is threatened due to frequent drought episodes. There has been much research aiming to understand the physiological, biochemical, and genetic basis of drought tolerance in potato as a basis for improving production under drought conditions. The complex phenotypic response of potato plants to drought is conditioned by the interactive effects of the plant's genotypic potential, developmental stage, and environment. Effective crop improvement for drought tolerance will require the pyramiding of many disparate characters, with different combinations being appropriate for different growing environments. An understanding of the interaction between below ground water uptake by the roots and above ground water loss from the shoot system is essential. The development of high throughput precision phenotyping platforms is providing an exciting new tool for precision screening, which, with the incorporation of innovative screening strategies, can aid the selection and pyramiding of drought-related genes appropriate for specific environments. Outcomes from genomics, proteomics, metabolomics, and bioengineering advances will undoubtedly compliment conventional breeding strategies and presents an alternative route toward development of drought tolerant potatoes. This review presents an overview of past research activity, highlighting recent advances with examples from other crops and suggesting future research directions.