Light, new particles may alter the transition frequencies between atomic levels. Constraining such new interactions by comparing measured frequencies with precise ab-initio calculations is feasible only for few-electron systems. For larger elements, I will present a data-driven approach to bound the mass of a new boson and its couplings to electrons and neutrons. This limit is set by the non-linearity of a so-called King plot of frequency shifts between several isotopes. In addition to an analysis of measured data, I will show projections for promising atoms and ions that have the potential to probe new parameter space. Moreover, I will translate the rather model-independent bounds to some New Physics models and highlight new directions using highly-excited Rydberg states and highly-charged ions.