There are many emerging technologies that are used for growing plants. I have explored the three main methods to determine which one I will use for my kitchen - planter concept.
Geoponics refers to the traditional method of growing plants. It uses natural biomatter (soil and dirt) as the medium in which seeds grow. This is the natural method for plants to grow, almost all plants will grow in this condition (save for plant which grow in water such as lily pads).
Hydroponics refers to growing plants in "water" or a liquid nutrient solution. Usually the water must be aerated, or it will only cover the roots partially, to allow the roots some exposed to oxygen. Clay tablets may also be used to regulate moisture around the plant. By submerging the plant's roots in water, the plant is able to absorb a higher percentage of nutrients from the solution than it would from the soil. This leads to faster growth rates and larger plants. However, the water must be changed frequently, and the plants risk becoming water logged; many plants do not grow well in these types of conditions leading to the opposite of the desired effect. If too much light reaches the nutrient solution, bacteria and algae may grow.
Aeroponics is a subset of Hydroponics; it uses the same nutrient solution to feed the plant but sprays the solution onto the roots instead of submerging the roots in it. By spraying the solution, the roots are exposed to more oxygen. This leads to an even higher growth rate and larger biomass produced. This method is suitable for large scale plant production, and can even be used in space / "zero-gravity" environments. Similar issues exist with this method; the moist environment may lead to bacteria growth.