We present our studies on nonequilibrium carrier dynamics in high temperature superconductors, using the optical pump-probe spectroscopy method. We have performed our time-resolved measurements of the optical reflectivity change ΔR/R in HgBa2Ca2Cu3O8-x (Hg-1223), Pb- and Gd-doped Bi2Sr2CaCu2O10-x (Bi-2212), and MgB2 thin-film and single-crystal superconducting samples. The measured optical signals were strongly related to the presence of a superconducting energy gap Δ in the electronic energy spectrum. The superconducting transition at the critical temperature Tc was also clearly observed. In Hg-1223 thin films, the ΔR/R signal measured in the superconducting state was only related to the Cooper pair-breaking and pair-formation dynamics, with no evidence of the phonon bottleneck effect, characteristic for conventional BCS materials. The pair-breaking time in Hg-1223 was measured to be ~350 fs and was temperature independent up to Tc. The quasiparticle recombination time was in the 5-10 ps range with the 1\Δ divergence at temperatures close to Tc and the 1\T divergence at low temperatures. In Bi-2212 single crystals, the Cooper pair dynamics below Tc was very similar to that observed in Hg-1223 films. Above Tc, however, we observed the change in the sign and shape of the ΔR/R signal, which we related to the presence of the pseudo-gap state. Finally, in MgB2 films and crystals, the temperature dependence of the amplitude of the superconducting component of the ΔR/R signal followed the Δ(T) anomalous temperature dependence, which was interpreted for our mixed clean\dirty MgB2 films as the two Δ's, closing at two different values of Tc's. The same two Tc's were also visible in the double-divergence of the temperature dependence of the electron-phonon relaxation time. The quasiparticle recombination time was on the order of 400 ps and was limited by the phonon escape time.