I will introduce a non-archimedean version of the link of a singularity. This object will be a space of valuations, a close relative of non-archimedean analytic spaces (in the sense of Berkovich) over trivially valued fields. After describing the structure of these links, I will deduce information about the resolutions of surface singularities. If times allows, I will then characterize those normal surface singularities whose link satisfies a self-similarity property. The last part is a joint work with Charles Favre and Matteo Ruggiero.