In view of future high-statistics data, it is useful to define a framework for precise determinations of the properties of the Higgs particle valid in generic extensions of the Standard Model. As I will discuss, this goal can be achieved with a limited set of so-called "Pseudo-Observables" (PO). The PO provides a systematic generalization of the "kappa-framework" so far adopted by the LHC experiments and provide a useful bridge between data and theory predictions. I discuss how the PO are defined and how they can be used to test various dynamical and symmetry hypotheses about the Higgs sector. The relation between PO and EFT couplings is also briefly discussed.