Arthur has given rather precise conjectures on the decomposition of the regular representation L^2(G(F)\\G(A)), where G is a simple Lie group over a number field F, with adele ring A. In particular, the irreducible constituents are partitioned into classes called Arthur packets. I will discuss the construction of some of these packets when G is the exceptional group $G_2$ and how one can justify that the constructed packets are the right ones.