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In its original version the KPZ equation models the dynamics of an interfacebordering a stable phase against a metastable one. Over past years thecorresponding two-dimensional field theory has been applied to models withdifferent physics. Out of a wide choice, the spin-spin time correlations forthe Heisenberg chain will be discussed at some length, also the equilibriumtime-correlations of the conserved fields for 1D fluids. An interesting recenttheoretical advance is the construction of the scale-invariant asymptotictheory, the so-called KPZ fixed point.

The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises