With the increase in the world’s population and per capita wealth, oil producers must not only increase edible oil production but also meet the demand for a higher quality and variety of products. Recently, the focus has shifted from single processing steps to the entire vegetable oil production process, with an emphasis on introducing innovative technologies to improve quality and production efficiency. In this review, conventional methods of oilseed storage, processing and extraction are presented, as well as innovative processing and extraction techniques. Furthermore, the parameters most affecting the products’ yields and quality at the industrial level are critically described. The extensive use of hexane for the extraction of most vegetable oils is undoubtedly the main concern of the whole production process in terms of health, safety and environmental issues. Therefore, special attention is paid to environmentally friendly solvents such as ethanol, supercritical CO2, 2-methyloxolane, water enzymatic extraction, etc. The state of the art in the use of green solvents is described and an objective assessment of their potential for more sustainable industrial processes is proposed.