T-linear resistivity and spectroscopy of hot metals and cold atoms: DMFT, SYK and beyond

Many materials with strong electronic correlations display metallic-like resistivity up to
very high temperature, with values exceeding the Mott-Ioffe-Regel (MIR) criterion (`bad metals').
Understanding transport in this regime,in relation to spectroscopic probes such as optical conductivity
and ARPES, raises the fundamental question of transport in regimes where long-lived quasiparticles
may not exist. Recently, cold atomic gases in optical lattices have offered a beautiful
experimental platform to investigate this question without the intervening effect of phonons.
Even more challenging is the crossover into a `strange metal' regime at lower temperatures,
in which resistivity becomes smaller than the MIR value while still departing from Fermi liquid behaviour.
I will review recent work on these questions in the context of Dynamical Mean Field Theory
and the Sachdev-Ye-Kitaev models, as well as high-temperature series expansions and
several computational approaches. I will emphasize some commonalities
between these approaches, and assess what is established at this point
and which questions are still open.