DisplayBank posted an interesting article detailing the current status of the OLED market and their forecasts for 2011-2016. DB says that the AMOLED market will enjoy fast growth in the near future, and will reach $17 billion in 2016:
Small displays will still be the largest sector in 2016, accounting for almost $12 billion. Medium displays will only account for about $1.5 billion. OLED TVs will enjoy a quicker growth - from only $200 million in 2012 to $3.9 billion in 2016. These numbers are quite in-line with forecasts by DisplaySearch ($20 billion in 2018) and iSupply (300 million small AMOLEDs shipped in 2015 and 2.1 million OLED TVs).
DB says that the biggest advantage of OLEDs will be the fact that it can be made flexible as it's not limited to a glass surface. This will revolutionize the industry, with a move from "part-based" display panel manufacturing (i.e. making rigid square display panels) to an "ingredient-based" production that will enable new product designs beyond what's available today.
Both Samsung and LG Display are getting ready to produce flexible shatter-proof OLEDs based on plastics (polyimide). Samsung promised first products in early 2012 while LG Display is reportedly building a development pilot line which will enable prototypes within 1-2 years.