Types of aquaponic systems can vary in their complexity, type of filtration, and other elements.
The most simple system for home-scale aquaponics would be the sun pond. Sun pond is a fish pond or a tank where the plants are floating (supported) on the water’s surface, with roots beneath the water. If you are raising omnivorous or herbivorous fish, the roots should ideally be physically protected, so the fish wouldn't damage them. The principle of sun pond resembles the ancient aquaponic technique used by the Aztecs.
A more complex aquaponic systems mostly have five main elements:
Settling basin for solid waste
Bio-filter for nitrification
Water pumps for circulating water
Note that the total number of basic elements may vary with the design. As aquaponic has been developed by many independent inventors all over the world, the concepts can vary greatly.
What makes a certain aquaponic setup stand out is the is the hydroponic system within it.
Most common production designs and methods for raising crops in hydroponic systems are:
Nutrient film technique (NFT)
Multiple methods can be combined. It's interesting that aquaponic systems are still mostly designed by farmers themselves. It is expected that as engineers and professional consultants will play a larger role as aquaponic projects get bigger and more complex, especially the commercial ones.