Understanding the internal structure of pseudoscalar mesons is at least as important in unraveling the working of quantum chromodynamics as hydrogen atom and its spectrum were to comprehend quantum electrodynamics. The $Q^2$ evolution of their electromagnetic and two-photon transition form factors from $Q^2 \to 0$ to its asymptotically large values helps us explore the infrared and ultraviolet behavior of quantum chromodynamics within one single observable. Schwinger-Dyson equations provide an ideal framework to study the internal (fundamental) degrees of a meson, \emph{i.e.}, quarks and gluons, as their derivation and structure requires no recourse to the coupling strength being small or large. We adopt a coupled formalism based on Schwinger-Dyson and Bethe-Salpeter equations to investigate light pseudoscalar meson form factors, making comparison with the experimental results whenever available and also discussing their implications for the tests of the Standard Model of particle physics.