  We review our recent results for production of $\eta_c(1S)$ and $\eta_c(2S)$
in the $\gamma^* \gamma^* \to \eta_c(1S,2S)$ fusion and in proton-proton
collisions via gluon-gluon fusion. The quarkonium wave functions are calculated
by solving Schr\"odinger equation for different $c \bar c$ potentials. Using
Terentev prescription the light-cone wave functions are obtained. The
light-cone wave functions are used then to calculate $\gamma^* \gamma^* \to
\eta_c$ transition form factors. The theoretical results are compared to the
Belle experimental data for $\eta_c(1S)$. In addition we discuss our results
for two-photon decay width. We present also results of our calculations for
proton-proton collisions obtained within $k_T$-factorization approach for
different unintegrated gluon distributions. The results for hadroproduction of
$\eta_c(1S)$ are compared to the LHCb experimental data.

High Energy Physics - Phenomenology