In the light-front view of nucleon structure the electromagnetic form factors are described in terms of frame-independent transverse densities of charge and magnetization. Recent work has studied the transverse densities at peripheral distances b = O(1/M_pi), where they are governed by universal chiral dynamics and can be computed using effective field theory (EFT). We summarize the main results and their physical interpretation. A new "mechanical" picture of peripheral nucleon structure is presented, based on the light-front formulation of chiral EFT. The large-N_c limit of QCD, the role of Delta intermediate states, and the range of applicability of chiral EFT in transverse nucleon structure are discussed. The chiral component of the transverse densities could be probed experimentally in elastic form factor measurements at very low Q2 (as planned at JLab 12 GeV). We also comment on the connection with GPDs and peripheral high-energy scattering processes.