Computational astrophysics has a long history, making astrophysics a major driver of algorithm and computer developments. Within the past two decades, computational astrophysics has seen a phase transition, from being dominated by individual researchers writing and running their own"private" simulations on their personal workstation, to large projects that gather experts from different fields and use the huge computational power available through parallel machines or GRID technologies. All these components make computational Astrophysics definitively an interdisciplinary field requesting the most sophisticated and advanced codes and resources. Due to the developments of numerous codes with an identical dedication to problems but different approaches, permanent discussions and code comparisons among the developers are urgent. The purpose of this JENAM Symposium, entitled " Grand challenges in computational astrophysics ", is to review where this very prolific research field stands.