We are interested in solving PDEs in domains partitioned into non-overlapping sub-regions featuring non-conforming interfaces. Non-conformity could be of discretization type when the mesh sizes and/or the local polynomial degrees inside the subdomains differ. Moreover, it could be of geometric type if the interfaces are curved and non-watertight. The Internodes method is an interpolation-based approach designed to deal with both geometric and discretization non-conforming interfaces. PDEs can be discretized inside each sub-domain by any Galerkin-based methods, like Finite Elements, Spectral Elements, or Isogeometric Analysis. Internodes was introduced in [1] and its convergence was analyzed in [2] for hp−fem. In particular, when the mesh sizes in the two adjacent subdomains decrease uniformly, then the method achieves optimal convergence in the broken-energy norm versus the maximum mesh size, exactly as the well-celebrated Mortar method does. Moreover, it has been proved that the Internodes method is conservative [3]. This means that it preserves some quantities, which are typical of the continuous solution of the specific PDE, at the interface of the decomposition. For instance, when solving linear elasticity problems, it preserves the balance of the forces and the null total work at the interface. The Internodes method has been applied with success to multiphysics problems, contact problems, and, recently, in the context of Reduced Basis Methods [4]. In this talk, I will present the Internodes method and its applications in different contexts, as a result of the collaboration with many co-authors: P. Africa, G. Anciaux, M. Bucelli, A. Dall'Olio, S. Deparis, D. Forti, A. Manzoni, F. Marini, A. Quarteroni, Y. Voet, F. Zacchei, E. Zappon. [1] S. Deparis, D. Forti, P. Gervasio, and A. Quarteroni. INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces. Computers & Fluids, 141:22–41, 2016. [2] P. Gervasio and A. Quarteroni. Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations. Comput. Methods Appl. Mech. Engrg., 334:138–166, 2018. [3] S. Deparis, P. Gervasio. Conservation of Forces and Total Work at the Interface Using the Internodes Method. Vietnam J. Math. 50:901–928, 2022. [4] E. Zappon, A. Manzoni, P. Gervasio, A. Quarteroni. A reduced order model for domain decompositions with non-conforming interfaces. J. Sci. Comp. 99, 22,