This thesis is devoted to the investigation of a new, large sample of brightest cluster galaxies (BCGs), their kinematic and stellar population properties and the relationships between these and the properties of the host clusters. Some of the questions addressed are: how the kinematic and stellar population properties differ from those of ordinary giant elliptical galaxies; and whether these properties are more influenced by the internal parameters of the BCGs or the properties of the host clusters. In order to do this, high signal-to-noise, long-slit spectra of 49 BCGs (concentrating on those classified as cD galaxies) in the nearby Universe were obtained with the Gemini and WHT telescopes. The radial velocity and velocity dispersion profiles were measured, and the Lick/IDS system of absorption indices was used to derive Single Stellar Population (SSP)-equivalent ages, metallicities and alpha-abundance ratios. A systematic comparison was made between the indices and derived parameters for this sample of BCGs and those of large samples of ordinary elliptical galaxies in the same mass range. The derived properties were tested for possible correlations with the internal properties of the galaxies (mass and luminosity) and the properties of the host clusters (density, mass, distance to X-ray peak and the presence of cooling flows). Clear rotation curves were found for a number of BCGs. In particular, NGC6034 and NGC7768 are rapidly rotating (> 100 km/s as measured from their major axis spectra), indicating that it is unlikely that they formed through dissipationless mergers. Velocity substructure in the form of kinematically decoupled cores was detected in 15 BCGs, and five BCGs were found with velocity dispersion increasing with radius. In general, the amount of rotation and the velocity substructure detected in this sample, and the position of the BCGs as a class of objects on the anisotropy--luminosity diagram, are similar to those of ordinary giant ellipticals in high density environments. No significant discrepancies between the index--velocity dispersion relations of this sample and those of normal ellipticals were found, but subtle differences between the derived SSP-parameters do exist. The BCGs show, on average, higher metallicity ([Z/H]) and alpha-abundance ([E/Fe]) values. The SSP-parameters! show very little dependence on the mass or luminosity of the galaxies, or the mass or density of the host clusters. The derived ages of these massive galaxies are consistent with being old, as expected. Overall, the star formation histories in BCGs, and the connection to the processes in the cluster centres, are very complex.