The desire for new mostly fluent “soft spaces” in architecture cannot be overseen any more. Therefore new tools and approaches are tried out to create architecture with special spatial qualities. Spatially curved membrane structures and especially anticlastic Minimal Surfaces offer one possible approach to this topic. This paper presents the overview of the research on spatially curved Minimal Surfaces that considers the infinite possibilities of membrane forms as elements in architecture in combination with common buildingtechnologies and shows the manifold possibilities of this approach and technology1. Further on this paper partly reveals new correlations between Minimal Surface and boundary conditions and so far unknown rules in its self organizing processes. Case studies document new capabilities in designing and creating space in architecture. Latest approaches are dealing with alternative boundary-conditions and with software implementation in terms of scripting found rules2.