Using resonant laser ionization, beta-decay studies, and for the first time mass measurements, three beta-decaying states have been unambiguously identified in 70Cu. A mass excess of -62 976.1(1.6) keV and a half-life of 44.5(2) s for the (6-) ground state have been determined. The level energies of the (3-) isomer at 101.1(3) keV with T(1/2)=33(2) s and the 1+ isomer at 242.4(3) keV with T(1/2)=6.6(2) s are confirmed by high-precision mass measurements. The low-lying levels of 70Cu populated in the decay of 70Ni and in transfer reactions compare well with large-scale shell-model calculations, and the wave functions appear to be dominated by one proton-one neutron configurations outside the closed Z=28 shell and N=40 subshell. This does not apply to the 1+ state at 1980 keV which exhibits a particular feeding and deexcitation pattern not reproduced by the shell-model calculations.