  The question of how soft polymers slide against hard surfaces is of
significant scientific interest, given its practical implications.
Specifically, such sytems commonly show interesting stick-slip dynamics,
wherein the interface moves intermittently despite uniform remote loading.
\mt{The year 2021 marked the 50$^{th}$ anniversary of the publication of a
seminal paper by Adolf Schallamach (\emph{Wear}, 1971)} that first revealed an
intimate link between stick-slip and moving detachment waves, now called
Schallamach waves. We place Schallamach's results in a broader context and
review subsequent investigations of stick-slip, before discussing recent
observations of solitary Schallamach waves. This variant is not observable in
standard contacts so that a special cylindrical contact must be used to
quantify its properties. The latter configuration also reveals the occurrence
of a dual wave -- the so-called separation pulse -- that propagates in a
direction opposite to Schallamach waves. We show how the dual wave and other,
more general, Schallamach-type waves can be described using continuum theory,
and provide pointers for future research. In the process, fundamental analogues
of Schallamach-type waves emerge in nanoscale mechanics and interface fracture.
The result is an on-going application of lessons learnt from Schallamach-type
waves to better understand these latter phenomena.
