Harder-Narasimhan filtration is a classical construction in algebraic geometry. It gives a canonical filtration for vector bundles on a regular projective curve. Similar constructions have been discovered in various contexts, such as geometry of numbers, p-adic Hodge theory, error correction codes etc, and it turns out that the proofs for the existence and uniqueness of Harder-Narasimhan filtration are of quite different natures in these contexts. In this talk, I will explain a joint work with Marion Jeannin, where we propose a framework of Harder-Narasimhan theory on a bounded lattice, which allows to give a unified proof for the existence and uniqueness of Harder-Narasimhan filtrations. In the end of the talk, I will explain an application of our method to coprimary decomposition, which was not known before as a Harder-Narasimhan filtration.