Closed geodesic nets are natural homological analogues of closed geodesics. We will present two curvature-free upper bounds for the length of a shortest non-trivial geodesic net in a closed Riemannian manifold. Then we are going to present analogous upper bounds for the smallest area of a minimal surface, as well as generalizations to the case of (singular) minimal submanifolds of arbitrary dimension. After that we are going to discuss the existence and classification of closed geodesic nets different from closed geodesics. This is a joint work with Regina Rotman.