Quantum nonlinear optics refers to a new physical regime where the electromagnetic re-sponse is not linear already at the level of single photons. We will discuss recent devel-opments in this field, new analysis tools, and future applications to light manipulation and to the study of many-body physics. A focus will be given to a current promising technique, where strong interaction between propagating photons is obtained via their coherent coupling to the strong electric-dipole of Rydberg atoms. A variety of engineered Hamiltonian dynamics will be presented, as well as recent demonstrations of photon blockade
and two-photon phase shifts.