  We investigate the Hall effect in two different theoretical models of
strongly correlated systems: a system made of weakly coupled Luttinger liquids,
in the presence of umklapp scattering, and the 2D triangular lattice, with
nearest-neighbor hopping and a local Hubbard interaction. In the first model we
use a memory function approach to compute the Hall coefficient as a function of
temperature and frequency in the presence of umklapp scattering. We find a
power-law correction to the free-fermion value (band value), with an exponent
depending on the Luttinger parameter $K_{\rho}$. At sufficiently high
temperature or frequency the Hall coefficient approaches the band value. We
discuss the applications to Hall experiments made in quasi 1D organic
compounds. In the second model, the complete temperature and doping
dependencies of the high-frequency Hall coefficient $\RH$ are evaluated
analytically and numerically for small, intermediate, and strong interactions
using various approximation schemes. We find that $\RH$ follows the
semiclassical $1/qn^*$ law near T=0, but exhibits a striking $T$-linear
behavior with an interaction- and doping-dependent slope at high temperature.
We compare our results with Hall measurements performed in cobaltates.
