By now, the foundations of loop quantum gravity are well understood. However, only a very limited number of predictions have been derived from full LQG due to the complicated nature of the dynamics. To tackle this problem it will be inevitable to further develop efficient numerical methods and construct effective models. In my talk I will discuss several recent approaches in which numerical methods play a key role. Amongst others I will discuss the semi-classical dynamics of cosmological states and symmetry reduction in the case of spherical symmetry.