Décalage was first introduced by Deligne in his work on Hodge theory and provides us with a way to construct a new filtered chain complex from an old one, in a certain way. Thinking of spectral sequences as a way to process the data available in a filtration, one can roughly think of the décalage machine as providing us with a way to encode “turning the page of a spectral sequence” or “taking the derived exact couple” on the level of filtrations. Although not originally phrased in this way, décalage can be made sense in terms taking connective covers of a filtration in a certain t-structure on the category of filtered complexes called the Beilinson t-structure. This allows one to generalise the construction also to filtered objects in other stable $infty$-categories, such as spectra. In this talk, we show that the language of the Beilinson t-structure and décalage provides access to highly structured results on filtered spectra and their associated spectral sequences. This is joint work with Achim Krause and Thomas Nikolaus.