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In this work, we investigate the dynamics of Scholte-Stoneley waves (SSWs) travelling along elastic metasurfaces, e.g. thin resonant structures embedding mechanical oscillators, placed at the interface between solid and fluid. To this purpose, an analytical dispersion law, valid in the long-wavelength regime, is derived and used to reveal the hybridization of SSWs with the collective resonance of the mechanical oscillators and the conversion of SSWs into leaky modes within the fluid. The analytical predictions are validated through numerical simulations that include both dispersive and harmonic analysis. Our findings disclose the capabilities of elastic metasurfaces in filtering, trapping and converting SSWs along fluid-solid interfaces, thus supporting the design of novel devices for solid-fluid interaction across various engineering applications, including microfluidics. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.