The aim of our work is to conduct rigorous analyses of subwavelength acoustic scattering problems and use these results to establish the mathematical foundations for the design of subwavelength metamaterials. We will present results that characterise a system's resonance in terms of the eigenpairs of the generalized capacitance matrix. We will then use this theory to explore applications including the design of cochlea-like metamaterials and enhanced sensors based on active metamaterials with exceptional points.