The structural and dielectric properties of Na0.5Bi0.5TiO3 (NBT) ceramics and crystals have been investigated and are compared to that of Pb(Zr0.55Ti0.45)O-3 (PZT55/45) and Pb(Mg1/3Nb2/3)(0.72)Ti0.28O3 (PMNT 72/28) ceramics. X-ray diffraction (XRD) profiles for (100), (110), (111), (200), (220), and (222) (referred to cubic structure) reveal that the monoclinic structure with Cc space group exists both in the NBT single crystal and ceramics. The diffraction profile obtained with high resolution laboratory XRD for the NBT single crystal can be well described, using Cc model instead of R3c model. The dielectric constant of NBT below T-hump shows some similarity to that of PZT45/55 ceramics below 50 degrees C in which oxygen octahedron rotations cause the frequency dispersion of the dielectric constant. The temperature-dependent dielectric constant for NBT can be deconvolved into two independent processes. The lower temperature process shows a typical relaxor characteristic and follows the Vogel-Fulcher relationship. The other process at higher temperature shows less frequency-dependent behavior. Comparing the dielectric constant of NBT with that of PZT55/45 and PMNT72/28 reveals that both oxygen octahedral rotations and random electric fields play an important role in the frequency dispersion of the dielectric constant for NBT relaxor feroelectric.