Despite the fact that the 3-body problem is an ancient conundrum that goes back to Newton, it is remarkably poorly understood, and is still a benchmark for modern developments. In this talk, I will give a (very) biased account of this classical problem, both from a modern theoretical perspective, i.e. outlining possible lines of attack coming from symplectic geometry, holomorphic curves and Floer theory; as well as comment on practical and numerical aspects, within the context of finding orbits for space mission design and ocean worlds exploration.