The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any infection will perpetually propagate regardless of the spreading rate. However, realworld networks are finite and experience indicates that infections do have a finite lifetime. In this chapter, we will provide with two new approaches to cope with the problem of concurrency and traffic in the spread of epidemics. We show that the epidemic incidence is shaped by contact flow or traffic conditions. Contrary to the classical assumption that infections are transmitted as a diffusive process from nodes to all neighbors,we instead consider the scenario in which epidemic pathways are defined and driven by flows. Extensive numerical simulations and theoretical predictions show that whether a threshold exists or not depends directly on contact flow conditions. Two extreme cases are identified. In the case of low traffic, an epidemic threshold shows up, while for very intense flow, no epidemic threshold appears. In this way, the classical mean-field theory for epidemic spreading in scale free networks is recovered as a particular case of the proposed approach. Our results explain why some infections persist with low prevalence in scale-free networks, and provide a novel conceptual framework to understand dynamical processes on complex networks.