In the high-energy limit, QCD can be formulated in terms of remarkably simple, yet non-trivial, structures. This regime is described by the so-called BFKL theory, which governs disparate QCD phenomena ranging from the rise of the gluon distribution function at small Bjorken-x to the analytic structure of multi-loop scattering amplitudes. In this talk, I will briefly review BFKL theory, with an emphasis on its implications for elastic scattering amplitudes. I will then discuss some of the still open questions and illustrate how recent three-loop amplitude calculations can help shedding a light on them.