This paper examines some of the consequences of the hypothesis that jets in all radio galaxies and quasars are relativistic on small scales, in the sense that the flow velocity >0.5c. This idea is suggested by a number of lines of evidence. Firstly, Unified Models (Urry & Padovani, 1995) imply that the relativistic motion required in core-dominated objects must also occur in a larger parent population consisting of most, if not all, extended sources. Secondly, superluminal motion is detected in the nuclei of extended sources and in the kpc-scale jet of M 87 (Hough, 1994; Biretta, Zhou & Owen, 1995). Thirdly, jets are one-sided in the same sense on pc and kpc scales; at all luminosities, the radio emission tends to become more symmetrical on larger scales, as expected if an initially relativistic flow decelerates (Bridle & Perley, 1984; Bridle et al., 1994a; Parma et al., 1994). Finally, depolarization asymmetry occurs in both low (Parma, de Ruiter & Fanti, 1996) and high (Laing, 1988; Garrington et al., 1988) luminosity sources: the implication is that the brighter jet is on the near side of the source. It is likely that the key difference between radio sources in the two morphological classes defined by Fanaroff & Riley (1974) are that relativistic flow persists to the extremities of FRII sources, but that FRI jets decelerate smoothly on intermediate scales (Laing, 1993; Bicknell, 1995). On kiloparsec scales, we can identify structures which we propose should be called fast jets. These are well-collimated and generally one-sided (in the sense that the jet/counterjet ratio >4:1). They also have longitudinal apparent magnetic field (B||). They occur both in FRII sources, and at the bases of FRI jets (Bridle & Perley, 1984). We suggest that they are relativistic flows, and that this fact is crucial to an understanding of their evolution. A framework for the understanding of the variety of extended structures in extragalactic radio sources in this context is illustrated in Figure 1, which is an improved version of the diagram presented by Laing (1993). A fast jet appears to be able to: decelerate and recollimate to form a slow jet with β << 1 (therefore two-sided unless external effects dominate); disrupt, as in wide-angle tail sources, or hit the external medium and form a hot-spot. Slow jets are probably formed only when a decelerating fast jet can be recollimated by the external pressure gradient (Phinney, 1983; Bowman, Leahy & Komissarov, 1995). This may not be possible for more powerful sources in flatter pressure gradients and it is likely that wide-angle tail sources are formed when a fast jet decelerates rapidly but cannot recollimate. Deceleration by entrainment is efficient when the jet is transonic, and Bicknell (1994) showed that this corresponds to β ≈0.3 − 0.7 for a relativistic jet. If the jet does not slow down sufficiently (e.g. by mass loading; Komissarov 1994), then the flow will remain supersonic until it impacts on the external medium, and an FRII source will result. The radio morphology is therefore determined by a combination of initial jet speed and thrust and the effects of the environment, via the rate of stellar mass loss and the pressure gradient. On the largest scales, a bridge(backflow) or tail (outflow) will be formed. If the jet remains supersonic as far as the end of the lobe (as in an FRII source), then it is inevitable that a backflow (bridge) will be generated. As emphasised by Parma, de Ruiter & Fanti (1996), the majority of FRI sources also show bridges: the residual momentum of the jets, their density contrast with the external medium and the external pressure gradient are all likely to be important in determining their large-scale morphologies.