Pulsars, are rotating and radiating neutron stars and are superb astrophysical laboratories of extreme physics. A typical neutron star has radius of ∼ 10 km, magnetic field of ∼ 1012 Gauss, density of ∼ 1017 kg/m3, rotating at a frequency ∼ 1 Hz and has a surface gravity of ∼ 1012m/s2. We observe pulsars as a sequence of periodic pulses mostly in the radio wavelength. What is mind-boggling is that the radio emission arises from a kilometer-sized emission patch which is at a distance of ∼ 1019 meter from us, and yet we see it!! The equivalent blackbody temperature of this radio emission is in the range 1025--1030 K, which exceeds the limit for any incoherent emission process. The physical mechanism of how this emission is generated is considered as one of the most challenging problems in astrophysics. In this talk I will discuss the wide spectrum of physical phenomena (like the QED phenomenon of magnetic pair creation, effect on the structure of neutron star surface, relativistic plasma dynamics etc) that takes place around the fast rotating, highly magnetized neutron star. These processes lead to generation of a highly relativistic flow of electron positron plasma in which we believe the radio emission is excited by a process called coherent curvature radiation, where charged ``bunches'' are accelerated in curved magnetic field. I will mention how evidence from high quality radio and X-ray observations of pulsars is putting stringent constraints to these ideas.
