In this paper we revise the three types of bipolarity recently proposed by Dubois and Prade, focussing on how the basic structure is being built up. In this way we can clarify key differences between them, and formalize to what extent some structures can be considered bipolar extensions. In particular, We stress the existence of alternative different concepts underlying their type II polarity, which may lead to different 3-valued structures, and the essential complexity underlying their type III polarity.