**7. Summary and Conclusions**

The *N* = 40 island of inversion, centered on 64Cr, has enjoyed intense attention from experimentalists and theorists alike. Experimental efforts at NSCL/MSU and RIBF/RIKEN have pushed the frontiers of spectroscopy by utilizing proton removal reactions which always lead to reaction residues more neutron-rich than the projectile. Technological advances, such as GRETINA at NSCL and MINOS at RIBF, allowed *γ*-ray spectroscopy, for the first time, at *N* = 46, *N* = 42 and *N* = 40 in the Fe, Cr, and Ti isotopic chains, respectively. On the theory side, the LNPS effective shell-model interaction continues to demonstrate not just the capability to reproduce the data but also to predict some of it. This close collaboration between experiment and theory has led to continuous refinements of the LNPS effective interaction and, in turn, motivated cutting-edge measurements at rare-isotope facilities around the world. Particularly exciting are predictions of an *N* = 50 island of inversion which rely on the monopole drifts from the LNPS interaction. This unmatched success of this effective interaction at *N* = 40 and beyond now lends confidence to these extrapolation and promises an exciting future for experiments at next generation rare-isotope facilities needed to reach these outskirts of the nuclear chart. In the *N* = 40 island of inversion itself, open challenges for experiment remain with respect to shape and configuration coexistence as predicted to be manifested in quadrupole-collective band

structures in 62,64Cr, for example. Also the study of such higher-lying off-yrast states has to remain a challenge for upcoming rare-isotope facilities. The future is exciting with experimental and theoretical advances in lockstep pushing the field forward to conquer the *N* = 50 island of inversion and fully characterize the *N* = 40 one. For this, more exotic fast-beam reactions such as the HI-induced charge exchange on high-spin projectiles [42] or multi-nucleon pickup reaction [53] may turn out to be promising tools in the arsenal of direct reactions.

**Funding:** Support from the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Grant No. DE-SC0020451 is acknowledged.

**Conflicts of Interest:** The author declares no conflict of interest.
