The internal structure of meson can be investigated by studying the electromagnetic form factor and the $\gamma^* \gamma^* - Quarkonium$ transition form factor. Recently, there has been a lot of interest in the exclusive production of mesons by photon fusion processes, especially in the $e^+ e^-$ colliders. This study is strongly motivated by the expectation that the cross-section measurement will give strong constraints on the parton structure of the meson. We will introduce a formalism of light-front quarkonium wave functions obtained from a solution of the Schrödinger equation for a selection of interquark potentials for $Q \bar Q$ interaction. We will present the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any $Q\bar Q$ pseudo-scalar, scalar, axial-vector and vector photon-meson transition. We will discuss the light-front wave function representation of the helicity form factors as functions of photon virtualities. We will discuss $\eta_c$, $\chi_{c0}$, $\chi_{c1}$, $\chi_{c2}$, and exotic state $\chi_{c1}(3872)$.