Seaweed has been cultured for decades (probably longer) along the coastlines of nations including China, Korea and Japan. Since the 1980's, much of the seaweed production from other asian nations has been harvested from wild stocks however in nations including the Philippines and Indonesia limited culture has taken place. Seaweed is harvested throughout the world as a food source as well as an export commodity for the production of agar and other derivative products.
Demand for seaweed and seaweed products has been greater than supply since the 1970's hence cultivation has since been viewed as the most effective means to increase production. Since this time seaweed farming has become increasingly economically viable and profitable and as a consequence its expansion has accelerated. It has been suggested that the farming of seaweed is both a means to improve economic conditions in developing nations and a means to reduce fishing pressures (this latter point seems to be related to the fact that seaweed provides protection and food to a variety of species ranging from snails to dugongs).
Although not a complete or totally comprehensive explanation on farming seaweed the following manual is a good resource for anyone interested in the methodologies required to successfully farm seaweed: Manual on Seaweed Farming