Low-lying excited states in 72 Ni have been investigated in an in-flight fission experiment at the RIBF facility of the RIKEN Nishina Center. The combination of the state-of-the-art BigRIPS and EURICA setups has allowed for a very accurate study of the β decay from 72 Co to 72 Ni, and has provided first experimental information on the decay sequence 72 Fe → 72 Co → 72 Ni and on the delayed neutron-emission branch 73 Co → 72 Ni. Accordingly, we report nearly 60 previously unobserved γ transitions which deexcite 21 new levels in 72 Ni. Evidence for the location of the so-sought-after (4 + 2 ), (6 + 2 ), and (8 + 1 ) seniority states is provided. As well, the existence of a low-spin β-decaying isomer in odd-odd neutron-rich Co isotopes is confirmed for mass A = 72. The new experimental information is compared to simple shell-model calculations including only neutron excitations across the fpg shells. It is shown that, in general, the calculations reproduce well the observed states.