The "Other" no soil method of growing plants is Hydroponics.  Hydroponics is a system of growing plants directly in water without any other growing medium.  NFT systems are very commonly used for this concept. Deep water culture is another method used for Hydroponics.  Hydroponics has been in existence for many centuries and is often coupled with fish farming to create Aquaponics.  For Hydroponics, nutrients are added to the water to feed the plants.  Certain types of plants tend to grow well in Hydroponic systems.  There are also plants that normally wouldnt be expected to grow well in hydroponic systems due to the height of the plants.  Hemp is an example of this type of plant.  Another type of farming that works well with hydroponics is the Dutch Bucket or Container method.  Hydroponics and Aquaponics are very similar in practice with the specific difference being how nutrients are produced/introduced for/to the plants.

40 Pot Hydroponic Tower