We present the results of an investigation of a 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. We have obtained high signal-to-noise, long-slit spectra of 49 BCGs in the nearby Universe with the Gemini and WHT telescopes. From this, we have measured the radial velocity and velocity dispersion profiles, and used the Lick system of absorption indices to derive Single Stellar Population (SSP)-equivalent ages, metallicities and α-abundance ratios. The results were systematically compared with those of large samples of ordinary elliptical galaxies in the same mass range. In addition, the derived properties were tested for possible correlations with the internal properties of the galaxies (mass, rotation and luminosity) and the properties of the host clusters (density, mass, distance to X-ray peak and cooling flows). We address the following questions: 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 clusters.