Olive (Olea europaea L.) is a crop of enormous economic and cultural importance. Over the years, the worldwide production of olive oil has been decreasing due to various biotic and abiotic factors. The current drop in olive oil production resulting from climate change raises concerns regarding the fulfillment of our daily demand for olive oil and has led to a significant increase in market prices. In the future, there will be a higher chance that we will face a severe shortage of olive oil, which could harm both the economic sector and the food supply. As olive groves cover more than 5 million hectares in the European Union alone, the need to preserve the crop in the context of extreme climatic events is imperative. As drought is considered one of the most limiting factors in agriculture, drought-resistant varieties and sustainable irrigation strategies are being developed to mitigate the impact of drought on crop productivity and secure the future supply of olive oil. This review focuses on recently gained insights into drought stress in olive trees through omics and phenomics approaches to unravelling mechanisms that may lead to developing new varieties that are tolerant against drought elicited by changes in growing systems.