Powerful extragalactic radio sources comprise two extended regions containing magnetic field and synchrotron-emitting relativistic electrons, each linked by a jet to a central compact radio source located in the nucleus of the associated galaxy. These jets are collimated streams of plasma that emerge from the nucleus in opposite directions, along which flow mass, momentum, energy, and magnetic flux. Methods of using the observations diagnostically to infer the pressures, densities, and fluid velocities within jets are explained. The jets terminate in the extended radio components, where they interact strongly with the surrounding medium through a combination of shock waves and instabilities. Jets may expand freely, be confined by external gas pressure, or be pinched by toroidal magnetic fields. Shear flows are known to be Kelvin-Helmholtz unstable and thus may be responsible for some of the observed oscillation of jets about their mean directions and for creating the turbulence and shock waves needed to accelerate the relativistic electrons. Larger-scale bending may be caused by changes in the jet axis within the nucleus, gravitational interaction of the radio galaxy with a companion galaxy, or rapid motion of the source through dense intergalactic gas. The compact radio sources also exhibit a jet morphology and contain more direct clues as to the origins of jets; in particular, the variations sometimes observed imply bulk flows that are relativistic. It is widely believed that nuclear activity is ultimately ascribable to gas accreting onto a massive black hole. The accretion can proceed in several different fashions, depending upon whether or not the gas has angular momentum and whether or not the radiation emitted is sufficiently intense to influence the dynamics of the flow. Several distinct mechanisms for jet production in the context of black holes have been proposed. (Alternative mechanisms involving dense star clusters and massive spinning stars are also reviewed.) Supersonic jets may be collimated along the spin axis of a gas cloud surrounding the source of the lighter jet gas. Magnetic fields may be crucial in collimating jets, especially if they are wrapped around the jet by orbiting gas and can thereby collimate the outflow through the pinch effect. In fact, the spin energy of the black hole could also be extracted by magnetic torques, in which case the jet would contain electrons and positrons and carry a large electromagnetic Poynting flux. Statistical investigations of active galaxies also furnish valuable information on their nature and evolutionary behavior. The formation of particular kinds of sources appears to be correlated with environmental effects and cosmic epoch. In addition, the brightest compact radio sources on the sky, which probably involve relativistic motion, may be intrinsically faint objects beamed in our direction. There is now compelling evidence for the continuous fueling of extragalactic radio sources through jets emerging from the nucleus of the associated galaxy. The morphological classification of radio sources is interpreted in terms of the powers, speeds, and surroundings of jets. The ratio of the mass accretion rate to the mass of the hole may determine whether an active nucleus will be primarily a thermal object like an optical quasar or a nonthermal object like a radio galaxy. The authors outline a unified model of nuclear activity and assess what future progress may stem from observational developments (especially the proposed very long baseline array), experimental approaches (such as wind tunnel simulations), and theoretical studies (in particular, large-scale numerical hydrodynamical computing).