  The purpose of this partly expository paper is to give an introduction to
modular forms on $G_2$. We do this by focusing on two aspects of $G_2$ modular
forms. First, we discuss the Fourier expansion of modular forms, following work
of Gan-Gross-Savin and the author. Then, following Gurevich-Segal and Segal, we
discuss a Rankin-Selberg integral yielding the standard $L$-function of modular
forms on $G_2$. As a corollary of the analysis of this Rankin-Selberg integral,
one obtains a Dirichlet series for the standard $L$-function of $G_2$ modular
forms; this involves the arithmetic invariant theory of cubic rings. We end by
analyzing the archimedean zeta integral that arises from the Rankin-Selberg
integral when the cusp form is an even weight modular form.
