Branching annihilating random walks are interacting particle systems that appear as a natural mathematical tool to model the spread of a population competing for spatial resources. The classical methods for proving survival heavily rely on monotonicity properties of the system and are therefore not applicable in this context. We consider a model on the lattice in which particles branch, perform jumps within a certain radius of their parent and are killed whenever they occupy the same site. We study the extinction and survival of the system under different parameter regimes and prove results about the particle density on the survival cluster. Based on joint works with Nina Gantert (TU Munich), Matthias Birkner (University of Mainz), Jiri Cérny (University of Basel) and Pascal Oswald (University of Basel).