`Preheating' refers to non-perturbative particle production at the end of cosmic inflation. In many modern inflationary models, this process is predominantly or partly tachyonic, that is, proceeds through a tachyonic instability where the mass-squared of the inflaton field is negative. An example of such a model is Higgs inflation, where the Standard Model Higgs field is the inflaton, formulated in Palatini gravity. The violent dynamics of such a strong instability can lead to strong production of gravitational waves and supermassive dark matter. I discuss the phenomenology of such models and the related CMB predictions.