Magnetars were originally observed as high-energy emitters as either soft gamma-ray repeaters (SGRs) or anomalous x-ray pulsars (AXPs). They are very active, mainly observed as x-ray sources, apparently very young and probably part of the general population of pulsars but with much larger magnetic fields. The origin of the large magnetic fields is unclear.

Stable neutron stars exist with masses approximately between one and two solar masses, and radii of approximately 10 to 11 km. The structure is determined primarily by a balance between gravitation and the repulsion between adjacent neutrons. The configuration depends on the equation of state of the neutron fluid. The rotation of the strong dipolar magnetic field generates a magnetosphere of charged particles, which co-rotates with the star.

Precision timing of pulses is at the heart of pulsar research. Pulse arrival times can be measured to an accuracy of only a few metres travel time, and analysis must take account of pulsar positions and the Earth’s orbit, the Römer correction to the barycentre, and General Relativistic corrections. Pulsar timing contributes to the comparison of fundamental positional reference frames. Timing provides periods and period changes on short and long time scales, giving pulsar ages and proper motions. The precision timing of some millisecond pulsars is comparable to the best terrestrial laboratory clocks.

Digitisation of incoming signals at nanosecond intervals allows complex manipulation of radio signals to provide for simultaneous multi-beam and multi-frequency operation. The periodic signals from pulsars must be extracted from background noise, allowing for frequency dispersion in propagation through the interstellar medium.

The remnant of a supernova explosion may be observed for some thousands of years in close relation to a pulsar. Radiation from a pulsar may excite radiation from the interstellar medium, causing a pulsar wind nebula, which may be asymmetric due to velocity of the pulsar

The radio and high-energy profiles show that the emitting regions are concentrated in gaps in the magnetosphere located over the magnetic poles and near the velocity of light cylinder. The radio sources of most normal pulsars are distributed unevenly over the polar cap and are highly concentrated, broadband and variable. Their excitation may move laterally, causing drifting in sub-pulse timing. Other radio emitters are located close to the gamma-ray emitters in the outer magnetosphere. Almost all radio pulses are highly polarised; the sweep of position angle in the radio pulses is related to the magnetic field at the location of the emitters.

Despite the extensive knowledge of the characteristics of the coherent radio emission, the mechanism is not understood. The high-energy radiation is incoherent and may be related to the flux of relativistic electrons and positrons in a current sheet at the boundary of the magnetosphere. The radio emission from the polar cap is at lower frequency at larger radii, as the magnetic field lines diverge. The emission may be affected by propagation through the polar cap; refraction along the magnetic field lines may increase the apparent pulse width at lower frequencies.

Advances in observing techniques, the commissioning of new radio telescopes and the prospect of the Square Kilometre Array are opening new fields of pulsar research. The 55 years since the discovery of pulsars have revealed a rich and evolving population and shown how precise timing can transform our understanding of neutron star structure, binary system dynamics, stellar populations and the interstellar medium, and have opened new prospects in general relativity physics. X-ray and gamma-ray telescopes, and Cerenkov shower arrays, are extending observations over the whole electromagnetic spectrum.

The majority of millisecond pulsars are in binary systems with white dwarfs or other neutron stars. Precision timing yields remarkably accurate orbital parameters and their evolution. Binary systems provide tests of relativistic effects including energy loss by gravitational waves.

Describes the diverse techniques used in telescopes for the very wide range of the electromagnetic spectrum covered by pulsar observations. Conventional telescopes for the visible range can be used with suitable high time resolution, while only the lowest energy x-rays can be focussed to form images. Higher x-ray and gamma-ray energies require individual photons to be detected and tracked. The highest energy gamma-rays are detected in Cerenkov air-shower arrays. In contrast to the photon detection of all high-energy radiation, radio telescopes and receivers treat radiation as waves with measurable amplitude and phase, allowing multiple beams to be formed in large phased arrays of radio telescopes.

The discovery of millisecond pulsars revealed an evolutionary sequence from normal binary stars to x-ray binaries and the millisecond binary pulsars. The companions of binary millisecond pulsars include other neutron stars and white dwarfs with various masses.

The ionised interstellar medium is ideally accessible to radio pulsar research, both on large scales through frequency dispersion and on small scales through scattering and random refraction of radio waves. The theory is presented both geometrically and as wave diffraction. Observations reveal structure on a wide range of scales, including the effects of discrete structures. Interstellar scattering also lengthens radio pulses.

The radiation from most pulsars has a high degree of linear polarisation, allowing measurements of Faraday rotation. Such radio observations of polarisation provide detailed measurements of the interstellar magnetic field along the line of sight to a pulsar, including the fields along the spiral arms and the large-scale field outside the plane of the Galaxy. Pulsars can probe the magnitude and direction of the galactic magnetic field.

Many of the masses of pulsars in binary systems are known to high accuracy from their dynamics, while the masses of solitary pulsars are difficult to obtain. Radii are available from x-ray luminosity where this is known to be thermal. This chapter assembles the known measurements of mass and radius for all neutron stars.