  Resistivity saturation is observed in many metallic systems with a large
resistivity, i.e., when the resistivity has reached a critical value, its
further increase with temperature is substantially reduced. This typically
happens when the apparent mean free path is comparable to the interatomic
separations - the Ioffe-Regel condition. Recently, several exceptions to this
rule have been found. Here, we review experimental results and early theories
of resistivity saturation. We then describe more recent theoretical work,
addressing cases both where the Ioffe-Regel condition is satisfied and where it
is violated. In particular we show how the (semiclassical) Ioffe-Regel
condition can be derived quantum-mechanically under certain assumptions about
the system and why these assumptions are violated for high-Tc cuprates and
alkali-doped fullerides.
