The recent [or not so much] economical crisis that forced Portugal to its knees and launched the country into a spiral of discredit has also forced the Portuguese into extra innovation and entrepreneurship. When getting some deserved sun this last June, on the beaches of Monte Gordo, Algarve, in the company of a great friend of mine, also a researcher, the subjects Aquaponics Hydroponics suddenly surfaced. Aquaponics??? I asked my friend, the marine biologist. I could have waited 'til later on and then ask my wife who has also graduated in Marine Biology, but I was way to curious to let it go just like that - a blur cloud in a sky of vague conversational topics.
He immediately told me that he's trying to start his own business, but still needs to optimize the whole system.
- What system?, I asked.
- What do you know about Aquaponics and Hydroponics?
- Aquaponics, Hydroponics, Catatonics! Not much, just that there is probably a system in it, if it is not the system itself... this ponics thing! I retorted comically.
And appreciating not only my interest on the subject, but also my remarkable humor, my friend started spitting stuff to my hears that I now very briefly reconstruct for you with this post. The answers to the questions I had were provided by five nice scientific articles I found on the web and are hereby listed on the bottom of the post, as usual. I'd highlight article five for anyone really wanting to go damn technical on this matter and engineer it in an optimized fashion; and I'd also like to emphasize the Aquaponics systems web page for a grandiose collection of amazing information!!!
What is Aquaponics and what's for?
Aquaponics is a bio-integrated system that links recirculating aquaculture with hydroponic vegetable, flower, and/or herb production... Recent advances by researchers and growers alike have turned aquaponics into a working model of sustainable food production. 
How does it work?
Aquaponics serves as a model of sustainable food production by following certain principles:
1) The waste products of one biological system serve as nutrients for a second biological system.
2) The integration of fish and plants results in a polyculture that increases diversity and yields multiple products. Water is reused through biological filtration and recirculation.
3) Local food production provides access to healthy foods and enhances the local economy. 
What are the typical organisms involved?
Tilapia is a warm-water species that grows well in a recirculating tank culture.  Plants grow rapidly with dissolved nutrients that are excreted directly by fish or generated from the microbial breakdown of fish wastes... some aquaponic systems have used channel catfish, largemouth bass, crappies, rainbow trout, pacu, common carp, koi carp, goldfish, Asian sea bass (barramundi) and Murray cod, most commercial systems are used to raise tilapia .
Does it really work?
Trials at the Freshwater Institute’s greenhouses showed that nitrogen, phosphorus, and other nutrients in aquaculture effluent can be effectively removed by plants grown in NFT hydroponics or constructed wetland systems. James Rakocy, Ph.D., and associates at the University of the Virgin Islands (UVI) developed a commercial-scale aquaponic system that has run continuously for more than five years .
Is it sustainable?
Sustainable indoor fish farming is the farming of the new millennium . Aquaponics increase economical efficiency because several key costs, such as nutrients, land and water are substantially reduced and component operating and infrastructural costs are shared. Lower resource requirements extend the geographic range of production to areas that rely heavily on food imports .
Utilizing data collected via a case study of an aquaponics operation in Milwaukee, Wisconsin... in temperate climates, tilapia and vegetable sales or, alternatively, yellow perch and vegetable sales are insufficient sources of revenue for this aquaponics system to offset regular costs when grown in small quantities and when operated as a stand-alone for-profit business. However, it is possible to reach economies of scale and to attain profitability with a yellow perch and lettuce system .
How to differ aquaponics from hydroponics?
Aquaponics is one method of hydroponics, and hydroponics is one method of greenhouse production . Aquaponics is essentially the combination of aquaculture and hydroponics .
Which method is best?
Production of 2.8 kg m-2 from the first hydroponic crop was similar to the 2.7 kg m-2 assessed in the high density aquaponic treatment. Conversely the 2.3 kg m-2 measured in the low density treatment was smaller. For the second trial no differences were noticed between the 6.0 kg m-2 measured in the hydroponic system and the 5.7 and 5.6 kg m-2 assessed in the high and low-density aquaponic treatments, respectively. Nevertheless different nutrient concentrations in water affected plant mineral composition. Aquaponic leaves were poorer in phosphorus but richer in calcium, potassium magnesium and sodium. 
 Diver, S., Rinehart, L. (2006). "Aquaponics - Integration of Hydroponics with culture". ATTRA - National Sustainable Agriculture Information, pp. 1-28
 Pantanella, E., Cardarelli, M., Colla, G., Rea, E., Marcucci, A. (2010). "Aquaponics VS. Hydroponics: Production and quality of lettuce crop". ISHS ACTA Horticulturae, 927, pp. unknown.
 Blidariu, F., Grozea, A. (2011). "Increasing the economical efficiency and sustainability of indoor fish farming by means of aquaponics - review". Animal Science and Biotechnologies, 44(2), pp. 1-7.
 Goodman, E. R. (2011). "Aquaponics: community and economic development". MIT Library Archives.
 Rakocy, J. E., Masser, M. P., Losordo, T. M. (2006). "Recirculating aquaculture tank production systems: Aquaponics - Integrating fish and plant culture". Southern Regional Aquaculture Center, pp. 1-16.
Figure 1 taken from Aquaponics systems, Home aquaponics system diy, [http://aquaponicssystems.landscapeideasandpicture.com/home-aquaponics-systems-diy/], last visited on the 16th of July 2014, last update unknown.