Cosmological first-order phase transitions are said to be supercooled when the nucleation temperature is much smaller than the critical temperature. They are typical of potentials which feature nearly scale-invariance, for which the bounce action decreases only logarithmically with time. The phase transition takes place slowly and the probability distribution of bubble nucleation time is maximally spread. Hubble patches which get percolated later than the average are hotter than the background after reheating and potentially collapse into primordial black holes (PBH). In the first part of the talk, I will discuss the formation of PBH by supercooled phase transitions. In the second part, I will discuss the search for supercooled phase transitions in pulsar timing arrays and how it affects the search for PBH in LIGO-Virgo.