  We review 15 years of theoretical and experimental work on the non-linear
response of glassy systems. We argue that an anomalous growth of the peak value
of non-linear susceptibilities is a signature of growing "amorphous order" in
the system, with spin-glasses as a case in point. Experimental results on
supercooled liquids are fully compatible with the RFOT prediction of compact
"glassites" of increasing volume as temperature is decreased, or as the system
ages. We clarify why such a behaviour is hard to explain within purely kinetic
theories of glass formation, despite recent claims to the contrary.
