  The pioneering computer simulations of the energy relaxation mechanisms
performed by Fermi, Pasta and Ulam can be considered as the first attempt of
understanding energy relaxation and thus heat conduction in lattices of
nonlinear oscillators. In this paper we describe the most recent achievements
about the divergence of heat conductivity with the system size in 1d and 2d
FPU-like lattices. The anomalous behavior is particularly evident at low
energies, where it is enhanced by the quasi-harmonic character of the lattice
dynamics. Remakably, anomalies persist also in the strongly chaotic region
where long--time tails develop in the current autocorrelation function. A modal
analysis of the 1d case is also presented in order to gain further insight
about the role played by boundary conditions.
