The main features of radiation received from pulsars imply that they are neutron stars which contain an extremely intense magnetic field and emit coherently in the radio domain. Most recent studies attribute the origin of the coherence to plasma instabilities arising in pulsar magnetospheres; they mainly concern the linear, or the nonlinear, character of the involved unstable waves.We briefly introduce radio pulsars and specify physical conditions in pulsar emission regions: geometrical properties, magnetic field, pair creation processes and repartition of relativistic charged particles. We point to the main ingredients of the linear theory, extensively explored since the 1970s: (i) a dispersion relation specific to the pulsar case; (ii) the characteristics of the waves able to propagate in relativistic pulsar plasmas; (iii) the different ways in which a two-humped distribution of particles may arise in a pulsar magnetosphere and favour the development of a two-stream instability.We sum up recent improvements of the linear theory: (i) the determination of a `coupling function' responsible for high values of the wave field components and electromagnetic energy available; (ii) the obtention of new dispersion relations for actually anisotropic pulsar plasmas with relativistic motions and temperatures; (iii) the interaction between a plasma and a beam, both with relativistic motions and temperatures; (iv) the interpretation of observed `coral' and `conal' features, associated with the presence of boundaries and curved magnetic field lines in the emission region; (v) the detailed topology of the magnetic field in the different parts of the emission region and its relation to models recently proposed to interpret drifting subpulses observed from PSR 0943+10, showing 20 sub-beams of emission.We relate the nonlinear evolution of the two-stream instability and development of strong turbulence in relativistic pulsar plasmas to the emergence of relativistic solitons, able to form elementary structures for pulsar radiation. We explain how nonlinear interactions between unstable waves and particles provide a canvas to explain `microstructures' (i.e. fluctuations on the microsecond timescale) observed in individual radio pulses and estimates for the level of electromagnetic energy reliable to pulsar radio emission.This emphasizes the importance of collective plasma effects in pulsar emission regions able to provide the degree of coherence required, to explain characteristic features of observed individual pulses and account for the high level of pulsar radio emission.This article was scheduled to appear in issue 5 of Plasma Phys. Control. Fusion. To access this Special issue please follow this link: http://www.iop.org/EJ/toc/0741-3335/45/5