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The epidemiology has recently witnessed great advances based on computational models. Its scope and impact are getting wider thanks to the new data sources feeding analytical frameworks and models. Besides traditional variables considered in epidemiology, large-scale social patterns can be now integrated in real time with multi-source data bridging the gap between different scales. In a hyper-connected world, models and analysis of interactions and social behaviors are key to understand and stop outbreaks. Big Data along with apps are enabling for validating and refining models with real world data at scale, as well as new applications and frameworks to map and track diseases in real time or optimize the necessary resources and interventions such as testing and vaccination strategies. Digital epidemiology is positioning itself as a discipline necessary to control epidemics and implement actionable protocols and policies. In this review we address the research areas configuring current digital epidemiology: transmission and propagation models and descriptions based on human networks and contact tracing, mobility analysis and spatio-temporal propagation of infectious diseases and infodemics that comprises the study of information and knowledge propagation. Digital epidemiology has the potential to create new operational mechanisms for prevention and mitigation, monitoring of the evolution of epidemics, assessing their impact and evaluating the pharmaceutical and non-pharmaceutical measures to fight the outbreaks. Epidemics have to be approached from the lens of complexity science as they require systemic solutions. Opportunities and challenges to tackle epidemics more effectively and with a human-centered vision are discussed here.