We study the modification of micromagnetic configurations in nanostructures, due to the Dzyaloshinskii-Moriya interaction (DMI) that appear at the interface of an ultrathin film. We show that this interaction leads to new micromagnetic boundary conditions that bend the magnetization at the edges. We explore several cases of ultrathin film nanostructures that allow analytical calculations (1D systems, domain walls, cycloids and skyrmions), compare with fully numerical calculations, and show that

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... a good physical understanding of this new type of micromagnetics can be reached. We particularly focus on skyrmions confined in circular nanodots and show that edges allow for the isolation of single skyrmions for a large range of the DMI parameter.