QCD instantons are arguably the best motivated yet unobserved nonperturbative effects predicted by the Standard Model. A discovery and detailed study of instanton-generated processes at colliders would provide a new window into the phenomenological exploration of QCD and a vastly improved fundamental understanding of its non-perturbative dynamics. We present for the first time a full calculation of QCD instanton-induced processes in proton-proton collisions accounting for quantum corrections due to both initial and final state gluon interactions. Although QCD instanton processes are predicted to be produced with a large scattering cross-section at small centre-of-mass partonic energies, discovering them at hadron colliders is a challenging task that requires dedicated search strategies. [Based on https://arxiv.org/abs/2010.02287 and https://arxiv.org/abs/1911.09726.] [for zoom link contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

I will give an introduction to the novel method of calculating scattering amplitudes in gauge theory with twistor-space string theory inspired rules. I will show how the method works in simple cases and discuss recent new results for the amplitudes obtained at tree and loop level. I'll discuss some known puzzles, the ways to resolve them, open questions and future directions, including issues in string theory, quantum field theory and phenomenology.