While the effects of climate change are already being felt in many parts of the world, societies are compelled to drastically rethink the way they produce and manage energy, to reduce the greenhouse-gases emissions associated to the sector. Urban areas are a critical piece of the puzzle to achieve the energy transition and reach the ambitious climate targets set out at global and European scales. Positive energy districts (PEDs), a new concept introduced in 2018 by the Strategic Energy Technology Plan, constitute a bottom-up response to this massive problematic and an opportunity to accelerate the transition towards low-carbon energy models in cities. However, their deployment is currently facing a set of diverse and complex challenges, mainly arising from their novelty and the lack of practical experience. In that context, the contribution of the present review of the literature is twofold. First, it seeks to provide a broad perspective of the advances of the research on PEDs with a special focus on applied studies and practical experiences. Then, it aims to identify substantial challenges that are currently slowing down PEDs effective operationalization, and study to what extent researchers and practitioners are currently approaching them. To that end, 135 papers are selected, categorized, and analysed according to their topics, locations, climates, districts, studied solutions and social concerns. As a result, the paper gives an overview of the main trends and necessities of PEDs research and practice and draws recommendations on how to adequately address identified challenges.