  We review recent results for the properties of doped antiferromagnets,
obtained by the numerical analysis of the planar t-J model using the novel
finite-temperature Lanczos method for small correlated systems. First we
shortly summarize our present understanding of anomalous normal-state
properties of cuprates, and present the electronic phase diagram,
phenomenological scenarios and models proposed in this connection. The
numerical method is then described in more detail. Following sections are
devoted to various static and dynamical properties of the t-J model. Among
thermodynamic properties the chemical potential, entropy and the specific heat
are evaluated. Discussing electrical properties the emphasis is on the optical
conductivity and the d.c. resistivity. Magnetic properties involve the static
and dynamical spin structure factor, as measured via the susceptibility
measurements, the NMR relaxation and the neutron scattering, as well as the
orbital current contribution. Follows the analysis of electron spectral
functions, being studied in photoemission experiments. Finally we discuss
density fluctuations, the electronic Raman scattering and the thermoelectric
power. Whenever feasible a comparison with experimental data is performed. A
general conclusion is that the t-J model captures well the main features of
anomalous normal-state properties of cuprates, for a number of quantities the
agreement is even a quantitative one. It is shown that several dynamical
quantities exhibit at intermediate doping a novel universal behaviour
consistent with a marginal Fermi-liquid concept, which seems to emerge from a
large degeneracy of states and a frustration induced by doping the
antiferromagnet.
