  We study transitions between distinct phases of one-dimensional periodically
driven (Floquet) systems. We argue that these are generically controlled by
infinite-randomness fixed points of a strong-disorder renormalization group
procedure. Working in the fermionic representation of the prototypical Floquet
Ising chain, we leverage infinite randomness physics to provide a simple
description of Floquet (multi)criticality in terms of a new type of domain wall
associated with time-translational symmetry-breaking and the formation of
`Floquet time crystals'. We validate our analysis via numerical simulations of
free-fermion models sufficient to capture the critical physics.
