In this talk, I will present a generalization of the Bondi framework for the description of asymptotically-flat spacetimes. This generalization is based on the relaxation of the hypersurface-orthogonality condition, which allows for the presence of a new parameter called the twist. The construction of a solution space in this context relies on the use of a combination of Newman-Penrose and metric formalisms which will be detailed. Importantly, the presence of the twist enables the identification of a rich and well-behaved subspace of algebraically special solutions, potentially opening new directions for their <a href="http://study.

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