  One-dimensional chains are used as a fundamental model of condensed matter,
and have constituted the starting point for key developments in nonlinear
physics and complex systems. The pioneering work in this field was proposed by
Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. An intense and
fruitful mathematical and physical research followed during these last 70
years. Recently, a fresh look at the mechanisms of thermalization in such
systems has been provided through the lens of the Wave Turbulence approach. In
this review, we give a critical summary of the results obtained in this
framework. We also present a series of open problems and challenges that future
work needs to address.
