Oil extraction
Seeds do vary a lot in their oil content and physical size. The oil extraction process must be optimized for every type of seed. What remains of the seed after the oil is extracted is called meal or cake.
Every oil extraction process heats up the oil in some way due to friction. However, temperatures over 150°C destroy the proteins and natural vitamin E in both the oil and the meal. Lower temperatures (in the 50°C to 70°C range, cold pressed) do not damage the oil or meal significantly, but do reduce the yield, making good oil a lot more expensive.
It is essential to retain vitamin E in the oil as it prevents the oil from oxidizing (getting rancid). Oil with little vitamin E tend to go rancid quickly unless treated with antioxidant chemicals. Refining the oil also takes out vitamin E.
Expeller pressed
An expeller is a kind of screw press. The oil is obtained by squeezing the seed, at pressures up to 15 tons per square inch. The higher the pressure, the more heat is generated. At extremely high pressures, the temperature can exceed 150°C. Expellers come with variations in design and operating mode. Some use steam or work in several stages (first press, second press). The steam is applied to increase the yield and destroy enzymes which will break down the oil into free fatty acids. The resulting meal can undergo the solvent extraction process as described below.

Cold pressed
The term cold pressed theoretically means that the oil is expeller-pressed at low temperatures and pressure. Sunflower and olives are the best candidates for this process. True cold-pressed oil is expensive and still contains minerals, phosphatides, vitamin E and is high in trace nutrients. Cold-Pressed oil is generally perceived as being healthier. The remaining cake from this process can be feedstock for solvent extraction.
Chemical or Solvent Extraction
The cheaper brands of oil (most regular commercial brands) generally use chemical solvents to extract the oil. The oil is separated from the pre-pressed cake with hexane or other petroleum solvents and then boiled to drive off the toxic solvents. The oil is next refined, bleached, and deodorized, which involves heating it to over 200°C. The oil extracted this way still contains some undesirable solvent residues, while the amounts of many key nutrients (especially vitamin E) are significantly reduced. The resulting product lacks flavor, aroma, pigments and nutrients. This oil, however, is ideal for biodiesel production.
Solvent extraction is used by big centralized industrial mills (up to 3000 t/d), while the extruder extraction is used by smaller decentralized oil mills (to about 25 t/d). With solvent extraction you can take out about 99,3% of the oil content in the seeds against 75-85% with a mechanical press alone.
The energy required for a solvent extractor is much higher as compared with cold pressing (470 kWh/t versus 27 - 135 kWh/t). Cold pressed oil does not always need to be refined before being sold as edible oil. The oil quality is depending on the quality of the seeds, type of expeller and finally the skills of the miller.
New technologies are being developed in order to be cleaner and minimize the energy input needed to extract the oil. A relatively new but still too expensive approach is using supercritical CO2 to replace the hexane as the solvent. CO2 is non-toxic and leaves no traces in the oil. It is used to obtain perfume oil from flowers.
Another advanced way is the use of an expander (see picture below). Expanders flake the seeds first and apply solvent extraction after in one integrated production line. Because the temperatures in this process do not exceed 105 degrees Celsius the nutritional value is still very high in both the oil and the meal. The machine also needs fewer workers, energy, steam, hexane and maintenance while in production. The color of the extracted oil and the produced meal from an expander are superior in quality compared to an extruder-solvent extraction plant. This translates to a better price when sold.