Spectral sequences have proven immensely powerful tools in modern mathematics. Unfortunately, they have gathered a, not completely unfounded, reputation of being ?difficult? and ?complicated?. This goal of this talk is act as an introduction to the construction of spectral sequences via the language of stable infinity categories. The focus lies on clarifying what is needed to put a multiplicative structure on spectral sequences. We will specifically look at the case of the Tate spectral sequence, a spectral sequence where multiplicativity is quite hard to pin down using old language, but where it is very straightforward in the infinity-categorical framework. This is all work in progress joint with Achim Krause and Thomas Nikolaus.