  Over the last decade, new developments in Similarity Renormalization Group
techniques and nuclear many-body methods have dramatically increased the
capabilities of ab initio nuclear structure and reaction theory. Ground and
excited-state properties can be computed up to the tin region, and from the
proton to the presumptive neutron drip lines, providing unprecedented
opportunities to confront two- plus three-nucleon interactions from chiral
Effective Field Theory with experimental data. In this contribution, I will
give a broad survey of the current status of nuclear many-body approaches, and
I will use selected results to discuss both achievements and open issues that
need to be addressed in the coming decade.
