Mass spectra and wave functions of the doubly heavy baryons are computed assuming that the two heavy quarks inside a baryon form a compact heavy ‘diquark core’ in a color anti-triplet, and bind with the remaining light quark into a colorless baryon. The two reduced two-body problems are described by the relativistic Bethe-Salpeter equations (BSEs) with the relevant QCD inspired kernels. We focus on the doubly heavy baryons with heavy diquark cores. After solving BSEs in the instantaneous approximation, we present the mass spectra and the relativistic wave functions of the diquark cores, and of the low-lying baryon states and with flavors , and . A comparison with other approaches is also made.