Radio pulsars: already fifty years

Although fifty years have passed 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 as yet no consensus on key issues, such as the nature of coherent radio emission or the conversion mechanism of the electromagnetic energy of the pulsar wind into particle energy. In this review, we present the main theoretical results on the magnetosphere of neutron stars. We formulate a number of apparently simple questions, which nevertheless remain unanswered since the very beginning of the field and which must be resolved before any further progress can be made.