This paper describes those properties of the host galaxies of powerful radio sources that are unique to radio galaxies. The radio galaxies have redshifts up to z = 0.5 and radio powers, P_408,MHz_, ranging from 10^25^ to 10^28^ W Hz^-1^ (H_0_=50 km s^-1^ Mpc^-1^ and q_0_ = 0.0). We find that the magnitudes, colors, and surface brightness profiles of these radio galaxies are very diverse. Their rest frame V magnitudes range from -24th to -20th magnitude and are 0.55 +/- 0.06 mag fainter than those of brightest cluster members. Their (B - V) colors can be as red as those of brightest cluster members but may also be ~1 mag bluer. The optical structure of the low-redshift (0.03 < z <0.25) radio galaxies may vary ranging from cD to N galaxy behavior. Although the host galaxies of the low-redshift radio sources are generally "elliptical-like" galaxies, a comparison of the overall structure of radio galaxies to those of radio- quiet "generalized elliptical galaxies" of Schombert shows that only 17% are genuine elliptical galaxies, 9% have elliptical profiles with truncated halos, 26% are roughly elliptical but have disturbed surface brightness profiles, 16% are cD or D galaxies, 7% have double nuclei, and 21% are N galaxies. The only property that radio galaxies, as a class, have in common is that their sizes are relatively larger than those of normal elliptical galaxies of the same absolute magnitude. At the 22d isophote (in V) radio galaxies are 11% larger, at the 24th isophote they are 15% larger, and at the 25th isophote they are 20% larger. The host galaxies of the low-redshift (0.03 <z <0.25) FR I and FR II sources have different properties. Sixty-nine percent of all FR I's are associated with cD-like or double nucleus galaxies, 19% with smooth ellipticals, and 13% with disturbed ellipticals; no FR I's are associated with N galaxies. Forty-one percent of all FR IIs are associated with N galaxies, 26% with smooth ellipticals, and 26% with disturbed ellipticals; no FR II's are associated with cD-like galaxies. The colors and color gradients are also different, with the FR II's having both bluer colors and a larger dispersion in their color gradients. Powerful FR I and FR II sources exhibit differing cosmological evolutions in their number counts. At low redshifts, almost all powerful sources are FR I's, and at high redshifts they are predominantly FR II's. We suggest that powerful FR I's prefer host galaxies that are the dominant central galaxies of relaxed groups and clusters, while FR II's are most often associated with violent galaxy encounters.