The formation and evolution of local brightest cluster galaxies (BCGs) is investigated by determining the stellar populations and dynamics from the galaxy core, though the outskirts and into the intracluster light (ICL). Integral spectroscopy of 23 BCGs observed out to 4 r e is collected and high signal-to-noise regions are identified. Stellar population synthesis codes are used to determine the age, metallicity, velocity, and velocity dispersion of stars within each region. The intracluster light (ICL) spectra are best modeled with populations that are younger and less metal-rich than those of the BCG cores. The average BCG core age of the sample is 13.3 ± 2.8 Gyr and the average metallicity is [Fe/H] = 0.30 ± 0.09, whereas for the ICL the average age is 9.2 ± 3.5 Gyr and the average metallicity is [Fe/H] = 0.18 ± 0.16. The velocity dispersion profile is seen to be rising or flat in most of the sample (17/23), and those with rising values reach the value of the host cluster's velocity dispersion in several cases. The most extended BCGs are closest to the peak of the cluster's X-ray luminosity. The results are consistent with the idea that the BCG cores and inner regions formed quickly and long ago, with the outer regions and ICL forming more recently, and continuing to assemble through minor merging. Any recent star formation in the BCGs is a minor component, and is associated with the cluster cool core status.