Understanding the mechanisms underlying characteristic dynamics and emergent behaviors in complex systems is increasingly gathering the interests of different research areas. Swarming behaviors have been first observed in nature, e.g. in swarms of insects, flocks of birds and schools of fish. However, this characteristic behavior is not only limited to the natural phenomena, but it is also spans to a wide range of applications, including pedestrians and traffic behaviors, social sciences and swarm robotics. In this talk I will give an overview of models at different scales recently developed for swarming dynamics exhibited by flocks of birds, with a specific focus on mathematical modelling of turning behaviors. One of the main feature of the phenomena investigated is that the emergent collective behavior is based on relatively simple local interaction rules between individuals, and typically there is no group leader that guides all the others in accomplishing their goal.Empirical evidence collected in real flocks seems to suggests that pairwise interactions do not depend on the relative euclidean metric distance between the agents involved, but on the number of individuals separating them. In the context of the so called topological interactions, starting from the microscopic scale, mesoscopic and macroscopic models have been rigorously derived under specific assumptions. Recent results obtained weakening assumptions will be presented. In particular the role of topological interactions in terms of convergence speed to consensus both for microscopic and macroscopic dynamics will be investigated. Numerical simulations in one- and two-dimensional domains give insights on the sensitive dependence of solutions with respect to initial conditions. The talk aims to provide an updated overview of the state of the art in mathematical modeling of swarm- ing, highlighting open challenges and research directions in both mathematical modelling and numerics research areas.