1.1. Historical perspective
In the 1970s and 1980s the powerful capabilities of radio interferometry gave birth to the study of extragalactic radio jets. It became clear that radio jets are plasma outflows originating in the centres of active galaxies, seen through their synchrotron emission. After much debate, properties such as the relative one-sidedness of the jets, and the measurement of apparent superluminal expansion, by Very Long Baseline Interferometry (VLBI), were accepted as due to the outflows having relativistic bulk speeds. Early attempts at unifying source populations based on special relativity and apparent source properties (e.g. 175) have developed over the years into comprehensive unified schemes (e.g. 8) whereby quasars are explained as radio galaxies whose jets are at small angles to the line of sight and so are boosted by relativistic effects.
By the mid 1990s, the study of radio jets had reached something of a hiatus, and major groups around the world turned their attention to other pursuits such as gravitational lensing and the study of the Cosmic Microwave Background (CMB) radiation. A turning point was the sensitivity and high-fidelity mirrors of the Chandra X-ray Observatory , which resulted in the detection of resolved X-ray emission from many tens of well-known extragalactic radio sources (see  for a source compilation as of 2006: the number continues to increase). When combined with X-ray measurements of the ambient gas made with Chandra and XMM-Newton, and multiwavelength data, many important questions related to the physics of jets can be addressed. Progress towards answering those questions is the substance of this review.
The enhanced capabilities for the X-ray study of jets have coincided with strong interest from the wider astronomical community in the growth of supermassive black holes (SMBHs), following the links that have been made between SMBH and galaxy growth (e.g. 165, 79). SMBHs (and indeed compact objects of stellar mass) commonly produce jets, as an outcome of accretion processes responsible also for black-hole growth. It is also clear that extragalactic jets are capable of transferring large amounts of energy to baryonic matter in the host galaxies and surrounding clusters at large distances from the SMBH. The way in which heating during the jet mode of AGN activity might overcome the problem of fast radiative cooling in the centre of clusters is now intensely studied in nearby objects (see Section 7), and heating from `radio mode' activity is included in simulations of hierarchical structure formation (e.g. 57). We need therefore to understand what regulates the production of jets and how much energy they carry. X-ray measurements of nuclear emission probe the fueling and accretion processes, and those of resolved jet emission and the surrounding gaseous medium probe jet composition, speed, dynamical processes, energy deposition, and feedback.a
1.2. Radiation processes
The two main jet radiation processes are synchrotron radiation and inverse-Compton scattering. Their relative importance depends on observing frequency, location within the jet, and the speed of the jet. The thermally X-ray-emitting medium into which the jets propagate plays a major rôle in the properties of the flow and the appearance of the jets. The physics of the relevant radiation processes are well described in published work (e.g. 86, 26, 153, 189, 168, 174, 137), and most key equations for the topics in this review, in a form that is independent of the system of units, can be found in .
It is particularly in the X-ray band that synchrotron radiation and inverse-Compton emission are both important. X-ray synchrotron emission depends on the number of high-energy electrons and the strength and filling factor of the magnetic field in the rest frame of the jet. Inverse Compton X-ray emission depends on the number of low-energy electrons, the strength of an appropriate population of seed photons (such as the CMB, low-energy jet synchrotron radiation, or emission from the central engine), and the geometry of scattering in the rest frame of the jet. In an ideal world, observations would be sufficient to determine the emission process, and this in turn would lead to measurements of physical parameters. In reality, X-ray imaging spectroscopy, even accompanied by good measurements of the multiwavelength spectral energy distribution (SED), often leaves ambiguities in the dominant emission process. Knowledge is furthered through intensive study of individual sources or source populations.
1.3. Generic classes of jets
In discussing jets, it is useful to refer to the Fanaroff and Riley  classification that divides radio sources broadly into two morphological types, FRI and FRII. A relatively sharp division between FRIs and FRIIs has been seen when sources are mapped onto a plane of radio luminosity and galaxy optical luminosity  - the so called Ledlow-Owen relation. FRIIs are of higher radio luminosity, with the separation between the classes moving to larger radio luminosity in galaxies that are optically more massive and luminous. The distinct morphologies (e.g. 150) are believed to be a reflection of different flow dynamics (e.g. 134).
FRI sources (of lower isotropic radio power, with BL Lac objects as the beamed counterpart in unified schemes) have broadening jets feeding diffuse lobes or plumes that can show significant gradual bending, usually thought to be due to ram-pressure as the source moves relative to the external medium. The jet emission is of high contrast against diffuse radio structures, implying that the jet plasma is an efficient radiator. kpc-scale jets are usually brightest at a flaring point some distance from the active galactic nucleus, and then fade gradually in brightness at larger distances from the core, although this pattern is often interrupted by bright knots seen when the jet is viewed in the radio or the X-ray. Such an example is shown in Figure 1 1. The jets are believed to slow from highly-relativistic to sub-relativistic flow on kpc-scales from entrainment of the external interstellar medium (ISM), perhaps enhanced by stellar mass loss within the jet. The strong velocity shear between the jet flow and the almost stationary external medium must generate instabilities at the interface , and drive the flow into a turbulent state. The physics of the resulting flow is far from clear, although it can be investigated with simplifying assumptions (e.g., 14, 15 and see Section 4).
Figure 1. Roughly 6.6 kpc (projected) of the inner jet of the z = 0.0165 FRI radio galaxy NGC 315. Left: 5 GHz VLA radio map showing a knotty filamentary structure in diffuse emission. Right: Smoothed Chandra X-ray image of ~ 52.3 ks livetime also showing knotty structure embedded in diffuse emission. The ridge-line defined by the radio structure is shown in white, and indicates a level of correspondence between the radio and X-ray knots. Figure adapted from .
FRII sources (of higher isotropic radio power, with quasars as the beamed counterpart in unified schemes) have narrower jets that are sometimes faint with respect to surrounding lobe plasma and that terminate at bright hotspots (Fig. 2). The jets are often knotty when observed with high resolution, and the jets can bend abruptly without losing significant collimation (see Section 3.1 and Section 5.3 for examples). The bending is often large in quasar jets, supporting the conjecture that quasars are viewed at small angle to the line of sight and that bends are amplified through projection. In contrast to FRI jets which are in contact with the external medium, the standard model for FRII jets is that they are light, embedded in lobe plasma, and remain supersonic with respect to the external gas out to the hotspots. The energy and momentum fluxes in the flow are normally expected to be sufficient to drive a bow shock into the ambient medium. The ambient gas, heated as it crosses the shock, forces old jet material that has passed through the hotspots into edge-brightened cocoons. FRII jets are thus low-efficiency radiators but efficient conveyors of energy to large distances. They are often hundreds of kpc in length (particularly when deprojected for their angles to the line of sight), crossing many scale heights of the external medium from relatively dense gas in a galaxy core to outer group or cluster regions where the external density and pressure are orders of magnitude lower. State-of-the-art three-dimensional magneto-hydrodynamical simulations that incorporate particle transport and shock acceleration do well at reproducing the essential characteristics of synchrotron emission from such a source, and suggest that the shock and magnetic-field structures of the hotspots and lobes are extraordinarily complex and unsteady [201, 202].
Figure 2. The z = 0.458 FRII radio galaxy 3C 200. A smoothed 0.3-5 keV Chandra X-ray image of ~ 14.7 ks livetime is shown with radio contours from a 4.86 GHz VLA radio map  (beam size 0.33" × 0.33"). Both nuclear  and extended X-ray emission are detected. A rough correspondence of some of the extended X-ray emission with the radio lobes has resulted in the claim for inverse-Compton scattering of the CMB by electrons in the lobes , but most of the extended emission over larger scales is now attributed to cluster gas .
1.4. Lifetimes and duty cycles
Individual FRI and FRII radio galaxies are thought to live for at most some tens of millions of years (e.g. 140, 118). Age estimates are based on measuring curvature in the radio spectra caused by radiative energy losses of the higher-energy electrons over the lifetime of the sources (e.g. 3). In contrast to the relative youth of observed radio structures, present-day clusters were already forming in the young Universe. Ideas that radio sources have an important rôle in heating cluster gas (see Section 7) then require a correct balance between the duty-cycle of repeated radio activity and heating efficiency as a function of jet luminosity. The duty cycle can be probed by searching for evidence of repeated activity from individual sources. Radio sources classified as GHz-Peaked Spectrum (GPS) or Compact Steep Spectrum (CSS) are small and believed to be either young or have their growth stunted by the external medium , and source statistics suggest that if they evolve to kpc-scale sizes they must dim while so doing . VLBI kinematic studies provide convincing evidence that sources in the Compact Symmetric Object (CSO) subset, at least, are young, with current ages less than 104 years . The fact that it is relatively uncommon to see GPS sources with extended radio emission that may be a relic of previous activity has been used to argue that periods between sustained activity are generally at least ten times longer than the radiative lifetime of the radio emission from the earlier activity . This is consistent with a time between episodes of activity in FRIIs of between about 5 × 108 and 109 years that is estimated using optical- and radio-catalog cross correlations coupled with an average source lifetime of about 1.5 × 107 years from modelling projected source lengths . Of course, within the lifetime of an individual radio source there might be shorter-term interruptions or variations of activity (see Section 8.1).
1 Values for the cosmological parameters of H0 = 70 km s-1 Mpc-1, m0 = 0.3, and 0 = 0.7 are adopted throughout this review. Back.