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Radio pulsars --- already fifty years!a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation b Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation Despite fifty years since the discovery of radio pulsars, there is still no satisfactory understanding of how these amazing objects operate. While there has been significant progress in understanding the basic properties of radio pulsars, there is yet no consensus on key issues such as the nature of coherent radio emission or the conversion mechanism of the electromagnetic energy of pulsar wind into particle energy. This review attempts to present the main theoretical results on the magnetosphere of neutron stars. A number of questions are formulated which, while seemingly fairly simple, have remained unanswered since the very beginning of the field and which should necessarily be resolved before any further progress can be made.
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