The VOLNA code for the numerical modeling of tsunami waves: generation, propagation and inundation. A novel tool for tsunami wave modeling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code VOLNA is able to handle the complete life cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains a detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. The majority of tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps, which are produced with these types of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally, the main conclusions are outlined and the perspectives for future research presented.