Increasing consciousness regarding the nutritional value of olive oil has enhanced the demand for this product and, consequently, the expansion of olive tree cultivation. Although it is considered a highly resilient and tolerant crop to several abiotic stresses, olive growing areas are usually affected by adverse environmental factors, namely, water scarcity, heat and high irradiance, and are especially vulnerable to climate change. In this context, it is imperative to improve agronomic strategies to offset the loss of productivity and possible changes in fruit and oil quality. To develop more efficient and precise measures, it is important to look for new insights concerning response mechanisms to drought stress. In this review, we provided an overview of the global status of olive tree ecology and relevance, as well the influence of environmental abiotic stresses in olive cultivation. Finally, we explored and analysed the deleterious effects caused by drought (e.g., water status and photosynthetic performance impairment, oxidative stress and imbalance in plant nutrition), the most critical stressor to agricultural crops in the Mediterranean region, and the main olive tree responses to withstand this stressor.