Stratifications are a classical tool to study singularities of real and complex algebraic varieties. Working in a larger field extension equipped with a valuation, I. Halupczok introduced a valuative variant which he called t-stratifications. He proved their existence and showed how they can be used to recover Whitney stratifications. In a joint work with I. Halupczok, we introduced some strengthenings of this notion and explored their relation with classical stratifications. In this talk I will give an informal introduction to these new concepts and present some of our main results. If time permits, I will briefly discuss some future dreams which partly motivated this project.