The notion of symmetry breaking has long been a valuable guiding principle to understand the behavior of physical systems at low energies. Accordingly, the Landau paradigm states that the effective description of infrared phases should be dictated by how global symmetries are realized by the ground state. In spite of being an intuitive and appealing idea, this paradigm has found multiple counterexamples along the decades. In this context, the notion of generalized global symmetries enabled the inclusion of many of these phases within a generalized Landau paradigm. In this talk, we will illustrate how this works when the broken symmetry does not correspond to an ordinary group-like symmetry, but rather to a non-invertible (or categorical) symmetry. In doing so, we will show that some standard concepts about symmetry breaking still hold within this context, whereas some others acquire an interesting twist. We will present a number of simple examples where the broken non-invertible symmetries are either of the discrete or the continuous type.