Are waves all localized in two dimensional random media?

It has been the dominant view for over two decades that all waves are localized in two dimensions for any given amount of disorder. Here, I would like to raise questions about this assertion. The discussion leads to the conclusion that there is a lack of the conclusive and definite support of the claim. Rather, the recent evidence tends to indicate that waves are not necessarily always localized in two dimensional random systems. Reasons are elaborated.