Higgs criticality in and beyond the Standard Model

Both parameters in the Higgs potential appear fine-tuned, relating to the hierarchy problem and the metastability of the electroweak vacuum. While such behavior is puzzling in conventional particle physics, it is a common feature of dynamical systems. This has motivated the conjecture that the values of the Higgs' parameters are the result of some dynamical mechanism. I will first review the interpretation of this as an example of near-criticality and give examples for dynamical mechanisms which have been proposed to achieve it. I will then give an overview over several projects aiming at demonstrating how this idea can be used for model building and phenomenology in both particle physics and Cosmology.