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.

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