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Impulsive gravitational waves in Minkowski space were introduced by RogerPenrose at the end of the 1960s, and have been widely studied over the decades.Here we focus on nonexpanding waves which later have been generalized toimpulses traveling in all constant-curvature backgrounds, i.e., the (anti-)deSitter universe. While Penrose's original construction was based on his vividgeometric "scissors-and-paste" approach in a flat background, until recently acomparably powerful visualization and understanding has been missing in thecase with a cosmological constant $\Lambda\not=0$. Here we review the originalPenrose construction and its generalization to non-vanishing $\Lambda$ in apedagogical way, as well as the recently established visualization: A specialfamily of global null geodesics defines an appropriate comoving coordinatesystem that allows to relate the distributional to the continuous form of themetric.

Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves