  In this manuscript, in honour of L. Kadanoff, we present recent progress
obtained in the description of finite dimensional glassy systems thanks to the
Migdal-Kadanoff renormalisation group (MK-RG). We provide a critical assessment
of the method, in particular discuss its limitation in describing situations in
which an infinite number of pure states might be present, and analyse the MK-RG
flow in the limit of infinite dimensions. MK-RG predicts that the spin-glass
transition in a field and the glass transition are governed by zero-temperature
fixed points of the renormalization group flow. This implies a typical energy
scale that grows, approaching the transition, as a power of the correlation
length, thus leading to enormously large time-scales as expected from
experiments and simulations. These fixed points exist only in dimensions larger
than $d_L>3$ but they nevertheless influence the RG flow below it, in
particular in three dimensions. MK-RG thus predicts a similar behavior for
spin-glasses in a field and models of glasses and relates it to the presence of
avoided critical points.
