We report on phonon properties and electronic transitions in CaCu3Ti4O12, a material which reveals a colossal dielectric constant at room temperature without any ferroelectric transition. The results of far- and midinfrared measurements are compared to those obtained by broadband dielectric and millimeter-wave spectroscopy on the same single crystal. The unusual temperature dependence of phonon eigenfrequencies, dampings, and ionic plasma frequencies of low-lying phonon modes is analyzed and discussed in detail. Electronic excitations below 4 eV are identified as transitions between full and empty hybridized oxygen-copper bands and between oxygen-copper and unoccupied Ti 3d bands. The unusually small band gap determined from the dc conductivity (similar to 200 meV) compares well with the optical results.