In recent decades, the demand for vegetables has increased significantly due to the blooming global population. Climate change has affected vegetable production by increasing the frequencies and severity of abiotic and biotic stresses. Among the abiotic stresses, drought and salinity are the major issues that possess severe threats on vegetable production. Many vegetables (e.g., carrot, tomato, okra, pea, eggplant, lettuce, potato) are usually sensitive to drought and salt stress. The defence mechanisms of plants against salt and drought stress have been extensively studied in model plant species and field crops. Better understanding of the mechanisms of susceptibility of vegetables to drought and salt stresses will help towards the development of more tolerant genotypes as a long-term strategy against these stresses. However, the intensity of the challenges also warrants more immediate approaches to mitigate these stresses and enhance vegetable production in the short term. Therefore, this review enlightens the updated knowledge of responses (physiological and molecular) against drought and salinity in vegetables and potentially effective strategies to enhance production. Moreover, we summarized different technologies such as seed priming, genetic transformation, biostimulants, nanotechnology, and cultural practices adopted to enhance vegetable production under drought and salinity stress. We propose that approaches of conventional breeding, genetic engineering, and crop management should be combined to generate drought and salt resistance cultivars and adopt smart cultivation practices for sustainable vegetable production in a changing climate.