Fruits and vegetables are rich sources of bioactive compounds and micronutrients. Some of the most abundant are phenols and carotenoids, whose consumption contributes to preventing the occurrence of degenerative diseases. Recent research has shown the potential of non-thermal processing technologies, especially pulsed electric fields (PEF), ultrasounds (US), and high pressure processing (HPP), to trigger the accumulation of bioactive compounds through the induction of a plant stress response. Furthermore, these technologies together with high pressure homogenization (HPH) also cause microstructural changes in both vegetable tissues and plant-based beverages. These modifications could enhance carotenoids, phenolic compounds, vitamins and minerals extractability, and/or bioaccessibility, which is essential to exert their positive effects on health. Nevertheless, information explaining bioaccessibility changes after non-thermal technologies is limited. Therefore, further research on food processing strategies using non-thermal technologies offers prospects to develop plant-based products with enhanced bioaccessibility of their bioactive compounds and micronutrients. In this review, we attempt to provide updated information regarding the main effects of PEF, HPP, HPH, and US on health-related compounds bioaccessibility from different vegetable matrices and the causes underlying these changes. Additionally, we propose future research on the relationship between the bioaccessibility of bioactive compounds and micronutrients, matrix structure, and non-thermal processing.