Pions and kaons are the lightest quark-antiquark bound states and simultaneously the pseudo-Goldstone bosons associated with dynamical chiral symmetry breaking. Understanding their internal structure is essential to comprehending the underlying theory of quantum chromodynamics (QCD). The Q2 evolution of their electromagnetic and two-photon transition form factors from Q2 -> 0 to its large values helps us explore the infrared and ultraviolet behavior of QCD within one single observable. Schwinger-Dyson equations (SDEs) provide an ideal framework to study hadrons in terms of the fundamental internal degrees of freedom, i.e., quarks and gluons, as their derivation requires no recourse to the coupling strength being small or large. Mesons being two-body bound states also require a relativistic Bethe-Salpeter equation (BSE) to study their internal structure. We adopt a coupled SDE/BSE based formalism to investigate the pion and kaon form factors, making comparison with experimental observations and predictions from other theoretical tools. We also touch upon implications of these results for the tests of the celebrated Standard Model of particle physics.