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This paper deals with recent, developments of topology optimization techniques for application in some new types of design problems. The emphasis is on recent work of the Danish research groups at Aalborg University and at the Technical University of Denmark and focus is on the central role that the choice of objective functions and design parameterization plays for a successful extension of the material distribution approach to new design settings and to new types of physics models. The applications that will be outlined encompass design of laminated composite structures, design for pressure loads, design in fluids, design in acoustics, and design in photonics. A short outline of other design optimization activities is also given.