In this talk we will discuss the existence and asymptotic behavior of solution to the Q-curvature problem in $\mathbb{R}^{n}$. The solutions satisfy a non-local differential equation with exponential non-linearity, generalizing the problem of Gaussian curvature in dimension 2. We first classify the solutions and give their asymptotics and then we prove the existence of non-spherical solutions to the problem. PS : this is a joint work with T.Jin, L.Martinazzi and J.Xiong.