The ability to control an incoming wave field in a sub-wavelength material is advantageous for several applications in wave physics as energy conversion, time reversal technology, coherent perfect absorbers, or sound- proofing among others. The solution of this challenge requires to solve a complex problem : reducing the geometric dimensions of the structure while increasing the density of states at low frequencies and finding the good impedance conditions for the desired control. In this talk I present the possibilities of a new type of sub-wavelength metamaterials based on the concept of slow sound propagation. This last type of metamaterials makes use of its strong dispersion for generating slow-sound conditions inside the material and, therefore, drastically decreasing frequency of the absorption peaks. Hence, the structure thickness becomes deeply sub-wavelength. These open systems, at the resonant frequency, are characterized by both the leakage rate of energy (i.e., the coupling of the resonant elements with the propagating medium) and the intrinsic losses of the resonator. We discuss in this talk, the different possibilities offered by the balance between the leakage and the losses to activate the condition of critical coupling for trapping the energy around the resonant elements and generating a maximum of energy absorption or to generate deep subwavelength diffusers, what we call metadiffusers.